Inversions:

- definition

- images of individual points, lines and circles

(You should be familiar with proofs of the theorems in the notes
& be able to tell where exactly a given line or circle will be mapped under inversion.)  

- inversion preserves angles 
(must know what exactly this statement means & be able to use it.
No need to memorize proof.)

Lobachevskian plane

-Poincare model: must know what it looks like (what are "lines", 
"isometries", etc.). Be able to interpret a statement from 
Euclidean geometry (such as, "given a line and a point not on the line, there exists a perpendicular dropped from the point to the line") in the setting of the Poincare model. Prove (simple) statements based on the first axioms, by checking those axioms and repeating proofs from Euclidean geometry. Understand why the 
5th postulate fails in the Lobachevskian plane.