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I have asked the question in MSE, but did not get an answer.

I am asking a soft question here. I am interested in learning about Hyperbolic Geometry. I have read the book named "Fuchsian Groups" by S. Katok. Mainly I am focused about Hyperbolic Geometry, Geometry and Topology of 3-manifolds, knot theory, etc. But before studying more advanced hyperbolic geometry, I want to complete a course in Riemann surfaces.

I know about that there are many books avaliable in online such as Rick Miranda, Griffiths and Harris, etc. But most of them are toward Algebraic Geometry. I am looking for books in Riemann surfaces towards hyperbolic geometry, Teichmuller theory, 3-manifolds etc. Also, it will be nice if it contains some exercises.

Please help me. Thanking in advanced.

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  • $\begingroup$ This book is quite nice (in French though) : store.cassini.fr/enseignement-des-mathematiques/… $\endgroup$
    – Nicolas Hemelsoet
    Commented Apr 3, 2021 at 18:27
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    $\begingroup$ J. Hubbard's Teichmuller Theory, vol. 1 develops the theory of Riemann surfaces from this point of view. $\endgroup$
    – Alexandre Eremenko
    Commented Apr 3, 2021 at 18:37
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    $\begingroup$ Please include a link to the m.se question here, and a link to this question there. $\endgroup$
    – Gerry Myerson
    Commented Apr 4, 2021 at 0:28

2 Answers 2

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I've skimmed "Mostly surfaces" by Rich Schwartz; it may be at the correct level. Here is a link to the book at the AMS bookstore:

https://bookstore.ams.org/stml-60/

and there is a preprint version at Rich's webpage.

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You should try: http://matrixeditions.com/ http://matrixeditions.com/#Teich1 http://matrixeditions.com/#Teich2

In the future hopefully there will be volumes 3 and 4.

Best regards!

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