first start at writing index/readME

docs/source/index.md

@@ -34,12 +34,43 @@ documentation/pymf.md
 
 ## What is pymf?
 
+Pymf is a Python package for finding mean-field corrections to the non-interacting part of a Hamiltonian. It is designed to be simple to use and flexible enough to handle a wide range of systems. Pymf works by solving the mean-field equations self-consistently.
+
+Finding a mean-field solution is a 4-step process:
+
+- Define the non-interacting and interacting part of the Hamiltonian separately as hopping dictionaries.
+- Combine the non-interacting and interacting parts togher with your filling into a `Model` object.
+- Provide a starting guess and the number of k-points to use the `solver` function and find the mean-field correction.
+- Add the mean-field correction to the non-interacting part to calculate the total Hamiltonian.
+
+```python
+import pymf
+
+model = pymf.Model(h_0, h_int, filling=filling)
+mf_sol = pymf.solver(model, guess)
+h_full = pymf.add_tb(h_0, mf_sol)
+```
+
 ## Why pymf?
 
+Here is why you should use pymf:
+
+* Minimal
+  It contains the minimum of what you need to solve mean-field equations.
+
+* Simple
+  The workflow is simple and straightforward.
+
+* Time-effective
+  As pymf uses tight-binding dictionaries as input and returns, you can calculate the mean-field corrections on a coarse grid, but use the full Hamiltonian on a fine grid for observables afterward.
+
+
 ## How does pymf work?
 
 ## What does pymf not do yet?
 
+* Superconductivity
+
 ## Installation
 
 ```bash