Adapted README

README.md

 pystencils
 ==========
 
+[![pipeline status](https://i10git.cs.fau.de/pycodegen/pystencils/badges/master/pipeline.svg)](https://i10git.cs.fau.de/pycodegen/pystencils/commits/master)
+[![coverage report](https://i10git.cs.fau.de/pycodegen/pystencils/badges/master/coverage.svg)](https://i10git.cs.fau.de/pycodegen/pystencils/commits/master)
+[coverage report](http://pycodegen.pages.walberla.net/pystencils/coverage_report)
+
 Run blazingly fast stencil codes on numpy arrays.
 
-![alt text](doc/img/logo.png)
+*pystencils* uses sympy to define stencil operations, that can be executed on numpy array.
+It runs faster than normal numpy code and even as Cython and numba.
+
+Here is a code snippet that computes the average of neighboring cells:
+```python
+import pystencils as ps
+import numpy as np
+
+f, g = ps.fields("f, g : [2D]")
+stencil = ps.Assignment(g[0, 0],
+                        (f[1, 0] + f[-1, 0] + f[0, 1] + f[0, -1]) / 4)
+kernel = ps.create_kernel(stencil).compile()
+
+f_arr = np.random.rand(1000, 1000)
+g_arr = np.empty_like(f_arr)
+kernel(f=f_arr, g=g_arr)
+```
+
+*pystencils* is mostly used for numerical simulations using finite difference or finite volume methods.
+It comes with automatic finite difference discretization for PDEs:
+
+```python
+c, v = ps.fields("c, v(2): [2D]")
+adv_diff_pde = ps.fd.transient(c) - ps.fd.diffusion(c, sp.symbols("D")) + ps.fd.advection(c, v)
+discretize = ps.fd.Discretization2ndOrder(dx=1, dt=0.01)
+discretization = discretize(adv_diff_pde)
+```
+
+Look at the [documentation](http://pycodegen.pages.walberla.net/pystencils) to learn more.
 
 
 Installation
 ------------
 
 ```bash
-export PIP_EXTRA_INDEX_URL=https://www.walberla.net/pip
 pip install pystencils[interactive]
 ```
 
@@ -32,4 +63,5 @@ pip install pystencils[interactive,gpu,doc]
 Documentation
 -------------
 
-Read the docs [here](http://software.pages.walberla.net/pystencils/pystencils)
\ No newline at end of file
+Read the docs [here](http://pycodegen.pages.walberla.net/pystencils) and
+check out the Jupyter notebooks in `doc/notebooks`.