TITLE: Books for hyperbolic geometry ( surfaces ) with exercises?
QUESTION [9 upvotes]: what are good books on hyperbolic geometry/hyperbolic surfaces that have good number of exercises, just to get a good understanding of the literature . I know John Ratcliffe's book will be one of them, but it is kind of encyclopedic. I particularly want to solve some exercises where they will be using free homotopy, isotopy, Arzela-Ascoli arguments, covering spaces, lifting of curves and homotopies, and will be actually using hyperbolicity of the manifold.
Thanks !

REPLY [3 votes]: John Stillwell's book The Geometry of Surfaces is best if you are an undergraduate; if you are a more advanced than that, or an advanced undergraduate, Thurston's book Three Dimensional Geometry and Topology is the best. Either Katok's Fuchsian groups or Hubbard's new Teichmueller Theory Vol. 1, would be reasonable alternatives to Thurston; or, even better, supplemental reading to Thurston on weekend nights with some wine.