Restructure documentation index

Switched from RestructuredText to MyST because it's easier.
Created sections in the left-hand sidebar as discussed.

docs/source/index.md

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+---
+title: PeakPerformance documentation
+---
+
+# Welcome to the PeakPerformance documentation!
+
+[![](https://img.shields.io/pypi/v/peak-performance)](https://pypi.org/project/peak-performance)
+[![](https://img.shields.io/badge/code%20on-Github-lightgrey)](https://github.com/JuBiotech/peak-performance)
+[![](https://zenodo.org/badge/DOI/10.5281/zenodo.10255543.svg)](https://zenodo.org/doi/10.5281/zenodo.10255543)
+
+
+``peak_performance`` is a Python toolbox for Bayesian inference of peak areas.
+
+It defines PyMC models describing the intensity curves of chromatographic peaks.
+
+Using Bayesian inference, this enables the fitting of peaks, yielding uncertainty estimates for retention times, peak height, area and much more.
+
+# Installation
+
+```bash
+pip install peak-performance
+```
+
+You can also download the latest version from [GitHub](https://github.com/JuBiotech/peak-performance).
+
+
+The documentation features various notebooks that demonstrate the usage.
+
+```{toctree}
+:caption: Tutorials
+:maxdepth: 1
+
+markdown/Installation
+markdown/Preparing_raw_data
+markdown/Peak_model_composition
+markdown/PeakPerformance_validation
+markdown/PeakPerformance_workflow
+markdown/Diagnostic_plots
+markdown/How_to_adapt_PeakPerformance_to_your_data
+```
+
+
+```{toctree}
+:caption: Examples
+:maxdepth: 1
+
+notebooks/Ex1_Simple_Pipeline.ipynb
+notebooks/Ex2_Custom_Use_of_PeakPerformance.ipynb
+notebooks/Ex3_Pipeline_with_larger_example_dataset.ipynb
+```
+
+
+In the following case studies we investigate certain aspects of peak modeling.
+
+```{toctree}
+:caption: Case Studies
+:maxdepth: 1
+
+notebooks/Investigation_doublepeak_separation.ipynb
+notebooks/Investigation_noise_sigma.ipynb
+```
+
+
+Below you can find documentation that was automatically generated from docstrings.
+
+```{toctree}
+:caption: API Reference
+:maxdepth: 1
+
+pp_models
+pp_pipeline
+pp_plots
+```