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I am doing a reading course this semester on Geometric Group Theory. I have been following A Course on Geometric Group Theory by Bowditch. The professor who is guiding me is not aware of good textbooks on Geometric Group Theory. I am looking for a supplement to Bowditch's book.

Initially I began reading the book Groups, Graphs and Trees: An Introduction to the Geometry of Infinite Groups by John Meier. Although this is a nicely written book, I found its approach (and the professor I am reading under agreed) too combinatorial. Could someone suggest sources, especially ones that develop the theory of hyperbolic groups and the related machinery in a self contained manner?

I should mention that I do not have command over French or Russian, so sources should be in English.

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    $\begingroup$ MathOverflow link $\endgroup$ – Juan S Mar 1 '12 at 6:48
  • $\begingroup$ I quite like de la Harpe's book "Topics in Geometric Group Theory", but I find it frustrating to look things up in. This is because it doesn't use the page numbers, just the section numbers, so if I wanted to look up, say, SQ-universal groups then they are in III.37, and looking this up is much more of a hassel than just saying p66. It is a small gripe, I know, but a very annoying one! $\endgroup$ – user1729 Mar 1 '12 at 9:58
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    $\begingroup$ de la Harpe's book is problematic in that it doesn't provide a lot of detail. It's more of a survey than a textbook. I think Ross Geoghegan's book is better in this regard. $\endgroup$ – Cheerful Parsnip Mar 1 '12 at 12:36
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    $\begingroup$ I would add the awesome Bridson-Haefliger, though that does a LOT more than just GGT. There is also another book by de la Harpe et al, the so called "Green book". It is in French, but most of the chapters have been translated to English, and you can find a copy very easily by googling. $\endgroup$ – user641 Mar 1 '12 at 16:00
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    $\begingroup$ You might try Jean-Pierre Serre's book "Trees" (brilliant!). Also the book entitled Generators and Relations for Discrete Groups, of Coxeter and Moser. Bit old, but worthy to read or browse. $\endgroup$ – Nicky Hekster Mar 1 '12 at 20:47
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Check out these notes: http://www.math.utah.edu/~sg/Papers/banff.pdf

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    $\begingroup$ I found Jim Howie's notes on Hyperbolic groups useful (although they do not go into too much detail, for example they only give a sketch proof of the solution to the conjugacy problem). They can be found here. $\endgroup$ – user1729 Jul 5 '12 at 10:09
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A great newer text is Office Hours With a Geometric Group Theorist.

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When I began studying geometric group theory, the class texts were Bridson and Haflinger's "Metric Spaces of Nonpositive Curvature," Pierre de la Harpe's "Sur les groupes hyperboliques d'après Mikhael Gromov" (in French). I found that Ratcliffe's "Foundations of Hyperbolic Manifolds" and Larry C. Grove's "Classical Groups and Geometric Algebra" help as far as getting used to seeing more elementary examples and results about groups and geometry. Also, Thurston's "Geometry and Topology of Three-Manifolds," although Ratcliffe covers most of the same material in what, I feel, can be a more accessible text.

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This lecture notes are quite useful: http://www.math.ethz.ch/~alsisto/LectureNotesGGT.pdf

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