# Introductory textbook on geometry of hyperbolic space

I am looking for an introductory textbook to the geometry of the hyperbolic space $$\mathbb{H}^n$$. The book should include explicit description of geodesics and horospheres in various models (hyperboloid, Poincaré, Klein).

Apologies if the question is not appropriate for this site.

I really like Ratcliffe’s account of the 3 models ($$H^n$$, $$U^n$$, $$B^n$$) in Foundations of Hyperbolic Manifolds (2006, Chap. 3–5). It has what you ask for, and also copious exercises and historical notes.