This is a collection of exercises, notes, and facts/proofs I think are nice :)
All errors are mine, and if I missed a relevant attribution please let me know.
Classification of the arithmetic subgroups of SO(n,1)
The asymptotic cone of the real Heisenberg group
When are one-parameter subgroups geodesics?
A proof of the Gauss lemma using valuations rather than quotients
The isometry group of a proper metric space acts properly
Betti numbers are quasi-isometry invariant among nilpotent groups
Determining a limit can be easy using subsubsequential convergence
The Bruhat-Tits tree of SL(2,Qp) and Borel's volume divisor