Books for Hyperbolic Geometry.

Question

I want to read hyperbolic geometry. Can any one suggest some good books on the topic.

Answer 1

A professor of mine suggested Euclidean and Non-Euclidean Geometries: Development and History by Marvin J. Greenberg when I asked him the same question.

Answer 2

There's a short one called "About Lobachevski's Geometry" By Smogorzhevski. I translated the name from the Spanish copy I have, so it could be called differently. Sadly, that's the only one I know, because I haven't studied a lot about this geometry, and all I know was from general or euclidean geometry books that had a couple of chapters about introduction to non-euclidean geometries. That book is for beginners though, so with the background you say you have, you won't have any trouble at all with that.

Answer 3

Geometry and Topology of Three-Manifolds by Bill Thurston, edited by Silvio Levy.

Answer 4

I can recommend Low-Dimensional Geometry by Francis Bonahon and Chapter 2 of Thurston's Three-Dimensional Geometry and Topology (ed. Levy).]

You could go on to Al Marden's Outer Circles or Benedetti and Petronio's Lectures on Hyperbolic Geometry if that whets your appetite.

Answer 5

You may enjoy Chapter 6 of Needham's Visual Complex Analysis.

Answer 6

The book by martelli "An introduction to geometric topology" is a nice one on Hyperbolic geometry.