Here is a version of the table of contents of Bowditch's lecture notes *[A course on geometric group theory][1]*. 

1. Group presentations, free groups, abelianisation.

2. Cayley graphs. 

3. Quasi-isometries and their invariants. 

4. Fundamental groups, covering spaces.

5. Hyperbolic geometry, the plane, the space, surfaces, three-manifolds. 

6. Hyperbolic spaces, trees, the four-point condition, exponential growth of distance, quasi-geodesics, Hausdorff distances, qi-invariance, hyperbolic groups and their properties.

7. Isoperimetric functions, linear bounds and hyperbolicity, qi-invariance, Dehn functions, the word problem. 

  [1]: https://projecteuclid.org/ebooks/mathematical-society-of-japan-memoirs/a-course-on-geometric-group-theory/toc/10.2969/msjmemoirs/016010000