Highly Recommended References for Hyperbolic Planes and Modular Surfaces

Question

I would be very grateful if one could suggest highly recommended references for Hyperbolic Planes and Modular Surfaces that provide a readable self-contained introduction to these concepts.

Answer 1

For references, you can use, for instance:

1. The book "Fuchsian groups" by S.Katok. It covers both hyperbolic geometry and the modular group.

2. Or the book Anderson, James W., Hyperbolic geometry, Springer Undergraduate Mathematics Series. London: Springer (ISBN 1-85233-934-9/pbk). xi, 276 p. (2005). ZBL1077.51008.

(but it only covers hyperbolic geometry and general discrete groups)

3. Or

Bedford, Tim (ed.); Keane, Michael (ed.); Series, Caroline (ed.), Ergodic theory, symbolic dynamics, and hyperbolic spaces. Lectures given at the workshop ”Hyperbolic geometry and ergodic theory”, held at the International Centre for Theoretical Physics in Trieste, Italy, 17-28 April, 1989, Oxford Science Publications. Oxford etc.: Oxford University Press,. xv, 369 p. (1991). ZBL0743.00040.

Chapters 1 and 5: Chapter 1 covers basics of hyerbolic geometry and Fuchsian groups while chapter 5 will deal with the modular group, symbolic dynamics and continuous fractions part of the story.

4. Or, freely available Pete Clark's lecture notes on Shimura curves here, lectures 0, 2, 3, 4.