diff --git a/StringMath.Tests/BooleanExprTests.cs b/StringMath.Tests/BooleanExprTests.cs
index cc13b4e..c5a3f41 100644
--- a/StringMath.Tests/BooleanExprTests.cs
+++ b/StringMath.Tests/BooleanExprTests.cs
@@ -20,6 +20,7 @@ public void Setup()
             _context.RegisterLogical(">", (a, b) => a > b, Precedence.Power);
             _context.RegisterLogical("<", (a, b) => a < b, Precedence.Power);
             _context.RegisterLogical("!", (a) => !a);
+            _context.RegisterFunction("if", (args) => args[0] > 0 ? args[1] : args[2]);
         }
 
         [Test]
@@ -56,6 +57,12 @@ public void Evaluate_Binary_Operation()
             _context.RegisterBinary("+", (a, b) => a + b);
             Assert.IsTrue("(3 + 5) > 7".EvalBoolean(_context));
         }
+
+        [Test]
+        public void Evaluate_Ternary_Operation()
+        {
+            Assert.IsTrue("if(5 > 2, {true}, {false})".EvalBoolean(_context));
+        }
     }
 
     static class BooleanMathExtensions
diff --git a/StringMath.Tests/MathExprTests.cs b/StringMath.Tests/MathExprTests.cs
index 670f5e1..2f43d6c 100644
--- a/StringMath.Tests/MathExprTests.cs
+++ b/StringMath.Tests/MathExprTests.cs
@@ -1,5 +1,6 @@
 using NUnit.Framework;
 using System;
+using System.Linq;
 
 namespace StringMath.Tests
 {
@@ -15,6 +16,9 @@ public void Setup()
             MathExpr.AddOperator("<>", (a, b) => double.Parse($"{a}{b}"), Precedence.Prefix);
             MathExpr.AddOperator("e", (a, b) => double.Parse($"{a}e{b}"), Precedence.Power);
             MathExpr.AddOperator("sind", a => Math.Sin(a * (Math.PI / 180)));
+            MathExpr.AddFunction("add", args => args.Sum());
+            MathExpr.AddFunction("sqrt", args => Math.Sqrt(args[0]));
+            MathExpr.AddFunction("if", args => args[0] > 1 ? args[1] : args[2]);
         }
 
         [Test]
@@ -79,6 +83,7 @@ public void Double_Conversion_Should_Evaluate_Expression()
         [TestCase("{a}", new[] { "a" })]
         [TestCase("2 * {a} - {PI}", new[] { "a" })]
         [TestCase("({a} - 5) * 4 + {E}", new[] { "a" })]
+        [TestCase("if({a} - 2, 1, 0) + {E}", new[] { "a" })]
         public void LocalVariables_Should_Exclude_Global_Variables(string input, string[] expected)
         {
             MathExpr expr = input;
@@ -90,6 +95,7 @@ public void LocalVariables_Should_Exclude_Global_Variables(string input, string[
         [TestCase("{a}", new[] { "a" })]
         [TestCase("2 * {a} - {PI}", new[] { "a", "PI" })]
         [TestCase("({a} - 5) * 4 + {E}", new[] { "a", "E" })]
+        [TestCase("if({a} / 2, 1, 0) + {E}", new[] { "a", "E" })]
         public void Variables_Should_Include_Global_Variables(string input, string[] expected)
         {
             MathExpr expr = input;
@@ -190,6 +196,17 @@ public void Evaluate(string input, double variable, double expected)
             Assert.AreEqual(expected, expr.Result);
         }
 
+        [Test]
+        [TestCase("add({a}, 2)", 1, 3)]
+        [TestCase("sqrt({a})", 4, 2)]
+        [TestCase("3 + sqrt({a})", 4, 5)]
+        public void Evaluate_Function(string input, double variable, double expected)
+        {
+            MathExpr expr = input.Substitute("a", variable);
+
+            Assert.AreEqual(expected, expr.Result);
+        }
+
         [Test]
         [TestCase("abs -5", 5)]
         [TestCase("abs(-1)", 1)]
@@ -368,5 +385,15 @@ public void Compile_Resolves_Global_Variables()
 
             Assert.AreEqual(1 + Math.PI, result);
         }
+
+        [Test]
+        public void Compile_Resolves_Function()
+        {
+            var expr = "1 + add(2, 3)".ToMathExpr();
+            var fn = expr.Compile();
+            double result = fn();
+
+            Assert.AreEqual(6, result);
+        }
     }
 }
diff --git a/StringMath/Expressions/IExpression.cs b/StringMath/Expressions/IExpression.cs
index 91b4bf2..f78d215 100644
--- a/StringMath/Expressions/IExpression.cs
+++ b/StringMath/Expressions/IExpression.cs
@@ -11,6 +11,8 @@ internal enum ExpressionType
         VariableExpression,
         /// <summary><see cref="Expressions.ConstantExpression"/>.</summary>
         ConstantExpression,
+        /// <summary><see cref="Expressions.InvocationExpression"/>.</summary>
+        Invocation,
     }
 
     /// <summary>Contract for expressions.</summary>
diff --git a/StringMath/Expressions/InvocationExpression.cs b/StringMath/Expressions/InvocationExpression.cs
new file mode 100644
index 0000000..50b80cf
--- /dev/null
+++ b/StringMath/Expressions/InvocationExpression.cs
@@ -0,0 +1,26 @@
+using System.Collections.Generic;
+using System.Linq;
+
+namespace StringMath.Expressions
+{
+    internal class InvocationExpression : IExpression
+    {
+        public InvocationExpression(string name, IReadOnlyCollection<IExpression> arguments)
+        {
+            Name = name;
+            Arguments = arguments;
+        }
+
+        public ExpressionType Type => ExpressionType.Invocation;
+
+        public string Name { get; }
+        public IReadOnlyCollection<IExpression> Arguments { get; }
+
+        /// <inheritdoc />
+        public override string ToString()
+            => ToString(MathContext.Default);
+
+        public string ToString(IMathContext context)
+            => $"{Name}({string.Join(", ", Arguments.Select(x => x.ToString()))})";
+    }
+}
diff --git a/StringMath/IMathContext.cs b/StringMath/IMathContext.cs
index 4234503..f49b6c1 100644
--- a/StringMath/IMathContext.cs
+++ b/StringMath/IMathContext.cs
@@ -19,6 +19,11 @@ public interface IMathContext
         /// <param name="operation">The implementation of the operator.</param>
         void RegisterUnary(string operatorName, Func<double, double> operation);
 
+        /// <summary>Registers a function implementation.</summary>
+        /// <param name="functionName">The name of the function.</param>
+        /// <param name="body">The implementation of the function.</param>
+        void RegisterFunction(string functionName, Func<double[], double> body);
+
         /// <summary>Evaluates a binary operation.</summary>
         /// <param name="op">The operator.</param>
         /// <param name="a">Left value.</param>
@@ -32,6 +37,12 @@ public interface IMathContext
         /// <returns>The result.</returns>
         double EvaluateUnary(string op, double a);
 
+        /// <summary>Invokes a function by name and returns the result.</summary>
+        /// <param name="name">The function name.</param>
+        /// <param name="args">The function arguments.</param>
+        /// <returns>The result.</returns>
+        double InvokeFunction(string name, params double[] args);
+
         /// <summary>Returns the precedence of a binary operator. Unary operators have <see cref="Precedence.Prefix"/> precedence.</summary>
         /// <param name="operatorName">The operator.</param>
         /// <returns>A <see cref="Precedence"/> value.</returns>
@@ -46,5 +57,10 @@ public interface IMathContext
         /// <param name="operatorName">The operator.</param>
         /// <returns>True if the operator is unary, false if it does not exist or it is binary.</returns>
         bool IsUnary(string operatorName);
+
+        /// <summary>Tells whether an identifier is a function.</summary>
+        /// <param name="functionName"></param>
+        /// <returns></returns>
+        bool IsFunction(string functionName);
     }
 }
diff --git a/StringMath/MathContext.cs b/StringMath/MathContext.cs
index 4f7b6ee..f69cafc 100644
--- a/StringMath/MathContext.cs
+++ b/StringMath/MathContext.cs
@@ -7,6 +7,7 @@ namespace StringMath
     /// <remarks>Inherits operators from <see cref="Parent"/>.</remarks>
     public sealed class MathContext : IMathContext
     {
+        private readonly Dictionary<string, Func<double[], double>> _functions = new Dictionary<string, Func<double[], double>>(StringComparer.Ordinal);
         private readonly Dictionary<string, Func<double, double, double>> _binaryEvaluators = new Dictionary<string, Func<double, double, double>>(StringComparer.Ordinal);
         private readonly Dictionary<string, Func<double, double>> _unaryEvaluators = new Dictionary<string, Func<double, double>>(StringComparer.Ordinal);
         private readonly Dictionary<string, Precedence> _binaryPrecedence = new Dictionary<string, Precedence>(StringComparer.Ordinal);
@@ -66,6 +67,10 @@ public bool IsUnary(string operatorName)
         public bool IsBinary(string operatorName)
             => _binaryEvaluators.ContainsKey(operatorName) || (Parent?.IsBinary(operatorName) ?? false);
 
+        /// <inheritdoc />
+        public bool IsFunction(string functionName)
+            => _functions.ContainsKey(functionName) || (Parent?.IsFunction(functionName) ?? false);
+
         /// <inheritdoc />
         public Precedence GetBinaryPrecedence(string operatorName)
         {
@@ -85,6 +90,15 @@ public void RegisterBinary(string operatorName, Func<double, double, double> ope
             _binaryPrecedence[operatorName] = precedence ?? Precedence.UserDefined;
         }
 
+        /// <inheritdoc />
+        public void RegisterFunction(string functionName, Func<double[], double> body)
+        {
+            functionName.EnsureNotNull(nameof(functionName));
+            body.EnsureNotNull(nameof(body));
+
+            _functions[functionName] = body;
+        }
+
         /// <inheritdoc />
         public void RegisterUnary(string operatorName, Func<double, double> operation)
         {
@@ -116,6 +130,17 @@ public double EvaluateUnary(string op, double a)
             return result;
         }
 
+        /// <inheritdoc />
+        public double InvokeFunction(string name, params double[] args)
+        {
+            double result = _functions.TryGetValue(name, out var fn)
+                ? fn(args)
+                : Parent?.InvokeFunction(name, args)
+                ?? throw MathException.MissingFunction(name);
+
+            return result;
+        }
+
         #region Factorial
 
         private static readonly Dictionary<double, double> _factorials = new Dictionary<double, double>
diff --git a/StringMath/MathException.cs b/StringMath/MathException.cs
index 4e17e0b..b203100 100644
--- a/StringMath/MathException.cs
+++ b/StringMath/MathException.cs
@@ -19,6 +19,8 @@ public enum ErrorCode
             UNEXISTING_VARIABLE = 4,
             /// <summary>Readonly variable.</summary>
             READONLY_VARIABLE = 8,
+            /// <summary>Missing function.</summary>
+            UNDEFINED_FUNCTION = 16,
         }
 
         /// <summary>Initializes a new instance of a <see cref="MathException"/>.</summary>
@@ -64,5 +66,8 @@ internal static Exception MissingVariable(string variable)
 
         internal static Exception ReadonlyVariable(string name)
             => new MathException(ErrorCode.READONLY_VARIABLE, $"Variable '{name}' is read-only.");
+
+        internal static Exception MissingFunction(string name)
+            => new MathException(ErrorCode.UNDEFINED_FUNCTION, $"Undefined function '{name}'.");
     }
 }
\ No newline at end of file
diff --git a/StringMath/MathExpr.cs b/StringMath/MathExpr.cs
index 39e1256..f14b713 100644
--- a/StringMath/MathExpr.cs
+++ b/StringMath/MathExpr.cs
@@ -194,6 +194,17 @@ public MathExpr SetOperator(string name, Func<double, double> operation)
             return this;
         }
 
+        /// <summary>Adds a new function or overwrites and existing one.</summary>
+        /// <param name="name">The name of the function.</param>
+        /// <param name="body">The code to execute for this function.</param>
+        /// <returns>The current math expression.</returns>
+        public MathExpr SetFunction(string name, Func<double[], double> body)
+        {
+            _cachedResult = null;
+            Context.RegisterFunction(name, body);
+            return this;
+        }
+
         /// <summary>Add a new binary operator or overwrite an existing operator implementation.</summary>
         /// <param name="name">The operator's string representation.</param>
         /// <param name="operation">The operation to execute for this operator.</param>
@@ -210,6 +221,12 @@ public static void AddOperator(string name, Func<double, double, double> operati
         public static void AddOperator(string name, Func<double, double> operation)
             => MathContext.Default.RegisterUnary(name, operation);
 
+        /// <summary>Adds a new function or overwrites and existing one.</summary>
+        /// <param name="name">The name of the function.</param>
+        /// <param name="body">The code to execute for this function.</param>
+        public static void AddFunction(string name, Func<double[], double> body)
+            => MathContext.Default.RegisterFunction(name, body);
+
         /// <inheritdoc cref="Substitute(string, double)"/>
         /// <remarks>Variables will be available in all <see cref="MathExpr"/> expressions.</remarks>
         public static void AddVariable(string name, double value)
diff --git a/StringMath/Parser/Parser.cs b/StringMath/Parser/Parser.cs
index 11aaa35..30788dd 100644
--- a/StringMath/Parser/Parser.cs
+++ b/StringMath/Parser/Parser.cs
@@ -1,4 +1,5 @@
 using StringMath.Expressions;
+using System.Collections.Generic;
 
 namespace StringMath
 {
@@ -70,22 +71,36 @@ private IExpression ParseBinaryExpression(IExpression? left = default, Precedenc
             return left;
         }
 
-        private IExpression ParsePrimaryExpression()
+        private IExpression ParsePrimaryExpression() => _currentToken.Type switch
         {
-            switch (_currentToken.Type)
-            {
-                case TokenType.Number:
-                    return new ConstantExpression(Take().Text);
+            TokenType.Number => new ConstantExpression(Take().Text),
+            TokenType.Operator when _mathContext.IsFunction(_currentToken.Text) => ParseInvocationExpression(),
+            TokenType.Identifier => new VariableExpression(Take().Text),
+            TokenType.OpenParen => ParseGroupingExpression(),
+            _ => throw MathException.UnexpectedToken(_currentToken),
+        };
+
+        private IExpression ParseInvocationExpression()
+        {
+            var fnName = Take().Text;
+
+            Match(TokenType.OpenParen);
 
-                case TokenType.Identifier:
-                    return new VariableExpression(Take().Text);
+            var arguments = new List<IExpression>(2);
 
-                case TokenType.OpenParen:
-                    return ParseGroupingExpression();
+            do
+            {
+                if (_currentToken.Text == ",")
+                    Take();
 
-                default:
-                    throw MathException.UnexpectedToken(_currentToken);
+                var argExpr = ParseBinaryExpression();
+                arguments.Add(argExpr);
             }
+            while (_currentToken.Text == ",");
+
+            Match(TokenType.CloseParen);
+
+            return new InvocationExpression(fnName, arguments);
         }
 
         private IExpression ParseGroupingExpression()
@@ -98,12 +113,9 @@ private IExpression ParseGroupingExpression()
             return expr;
         }
 
-        private Token Match(TokenType tokenType)
-        {
-            return _currentToken.Type == tokenType
-                ? Take()
-                : throw MathException.UnexpectedToken(_currentToken, tokenType);
-        }
+        private Token Match(TokenType tokenType) => _currentToken.Type == tokenType
+            ? Take()
+            : throw MathException.UnexpectedToken(_currentToken, tokenType);
 
         private Token Take()
         {
@@ -112,9 +124,7 @@ private Token Take()
             return previous;
         }
 
-        private bool IsEndOfStatement()
-        {
-            return _currentToken.Type == TokenType.EndOfCode;
-        }
+        private bool IsEndOfStatement() 
+            => _currentToken.Type == TokenType.EndOfCode;
     }
 }
\ No newline at end of file
diff --git a/StringMath/Parser/TokenType.cs b/StringMath/Parser/TokenType.cs
index 21f6bf9..c1b063e 100644
--- a/StringMath/Parser/TokenType.cs
+++ b/StringMath/Parser/TokenType.cs
@@ -11,6 +11,7 @@ internal enum TokenType
 
         /// <summary>[aA-zZ_]+[aA-zZ0-9_]</summary>
         Identifier,
+
         /// <summary>1 or .1 or 1.1</summary>
         Number,
 
diff --git a/StringMath/StringMath.csproj b/StringMath/StringMath.csproj
index f330116..78e7cbe 100644
--- a/StringMath/StringMath.csproj
+++ b/StringMath/StringMath.csproj
@@ -12,8 +12,8 @@ Supports variables and user defined operators.</Description>
     <PackageProjectUrl>https://github.com/miroiu/string-math</PackageProjectUrl>
     <RepositoryUrl>https://github.com/miroiu/string-math</RepositoryUrl>
     <PackageTags>expression-evaluator calculator string-math math string-calculator user-defined-operators operators custom-operators</PackageTags>
-    <Version>4.1.2</Version>
-    <PackageReleaseNotes>Fixed compiled expressions not using variables that are not passed as arguments</PackageReleaseNotes>
+    <Version>5.0.0</Version>
+    <PackageReleaseNotes>Added user defined functions</PackageReleaseNotes>
     <PackageLicenseFile></PackageLicenseFile>
     <GenerateDocumentationFile>true</GenerateDocumentationFile>
     <Nullable>enable</Nullable>
diff --git a/StringMath/Visitors/CompileExpression.cs b/StringMath/Visitors/CompileExpression.cs
index c808249..0e565cd 100644
--- a/StringMath/Visitors/CompileExpression.cs
+++ b/StringMath/Visitors/CompileExpression.cs
@@ -44,6 +44,7 @@ public Expression Visit(SM.IExpression expression)
                 SM.ConstantExpression constantExpr => VisitConstantExpr(constantExpr),
                 SM.UnaryExpression unaryExpr => VisitUnaryExpr(unaryExpr),
                 SM.VariableExpression variableExpr => VisitVariableExpr(variableExpr),
+                SM.InvocationExpression invocationExpr => VisitInvocationExpr(invocationExpr),
                 _ => throw new NotImplementedException($"'{expression?.GetType().Name}' Convertor is not implemented.")
             };
 
@@ -75,5 +76,15 @@ private Expression VisitUnaryExpr(SM.UnaryExpression unaryExpr) =>
                 nameof(IMathContext.EvaluateUnary),
                 null,
                 Expression.Constant(unaryExpr.OperatorName), Visit(unaryExpr.Operand));
+
+        private Expression VisitInvocationExpr(SM.InvocationExpression invocationExpr)
+        {
+            var args = invocationExpr.Arguments.Select(Visit).ToArray();
+            return Expression.Call(_contextParam,
+                nameof(IMathContext.InvokeFunction),
+                null,
+                Expression.Constant(invocationExpr.Name),
+                Expression.NewArrayInit(typeof(double), args));
+}
     }
 }
diff --git a/StringMath/Visitors/EvaluateExpression.cs b/StringMath/Visitors/EvaluateExpression.cs
index be04eef..6e1a828 100644
--- a/StringMath/Visitors/EvaluateExpression.cs
+++ b/StringMath/Visitors/EvaluateExpression.cs
@@ -1,4 +1,5 @@
 using StringMath.Expressions;
+using System.Linq;
 
 namespace StringMath
 {
@@ -43,5 +44,17 @@ protected override IExpression VisitVariableExpr(VariableExpression variableExpr
                 ? new ConstantExpression(value)
                 : throw MathException.UnassignedVariable(variableExpr);
         }
+
+        protected override IExpression VisitInvocationExpr(InvocationExpression invocationExpr)
+        {
+            var args = invocationExpr.Arguments
+                .Select(Visit)
+                .Cast<ConstantExpression>()
+                .Select(x => x.Value)
+                .ToArray();
+
+            double result = _context.InvokeFunction(invocationExpr.Name, args);
+            return new ConstantExpression(result);
+        }
     }
 }
diff --git a/StringMath/Visitors/ExpressionVisitor.cs b/StringMath/Visitors/ExpressionVisitor.cs
index 24a7157..1d04aa3 100644
--- a/StringMath/Visitors/ExpressionVisitor.cs
+++ b/StringMath/Visitors/ExpressionVisitor.cs
@@ -16,6 +16,7 @@ public IExpression Visit(IExpression expression)
                 ConstantExpression constantExpr => VisitConstantExpr(constantExpr),
                 UnaryExpression unaryExpr => VisitUnaryExpr(unaryExpr),
                 VariableExpression variableExpr => VisitVariableExpr(variableExpr),
+                InvocationExpression invocationExpr => VisitInvocationExpr(invocationExpr),
                 _ => expression
             };
 
@@ -29,5 +30,7 @@ public IExpression Visit(IExpression expression)
         protected virtual IExpression VisitBinaryExpr(BinaryExpression binaryExpr) => binaryExpr;
 
         protected virtual IExpression VisitUnaryExpr(UnaryExpression unaryExpr) => unaryExpr;
+
+        protected virtual IExpression VisitInvocationExpr(InvocationExpression invocationExpr) => invocationExpr;
     }
 }
diff --git a/StringMath/Visitors/ExtractVariables.cs b/StringMath/Visitors/ExtractVariables.cs
index 7db512e..6d1c5fa 100644
--- a/StringMath/Visitors/ExtractVariables.cs
+++ b/StringMath/Visitors/ExtractVariables.cs
@@ -31,5 +31,15 @@ protected override IExpression VisitVariableExpr(VariableExpression variableExpr
 
             return variableExpr;
         }
+
+        protected override IExpression VisitInvocationExpr(InvocationExpression invocationExpr)
+        {
+            foreach(var arg in invocationExpr.Arguments)
+            {
+                Visit(arg);
+            }
+
+            return invocationExpr;
+        }
     }
 }