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

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What is your background? – user38268 Jan 10 '13 at 11:13
I have knowledge in complex analysis, basic functional analysis, topology,basic algebra – Phani Raj Jan 10 '13 at 11:17

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

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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.

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

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There's 56-page introductory paper on hyperbolic geometry by Cannon, Floyd, Kenyon, and Parry which is absolutely excellent. You can download it from Kenyon's web page:

Cannon, Floyd, Kenyon, and Parry, Hyperbolic Geometry.

Note that this paper is much more directed towards the modern point of view than most sources, and is not at all interested in synthetic (or axiomatic) geometry.

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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.

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I think you mean the booklet (70 pages only) A.S. Smogorzhevski called "Lobachevskian Geometry" published by MIR Publishers Moscow. It is a nice booklet, but to short to be a good introduction – Willemien Aug 30 '15 at 20:43

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

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