Prerequisites for the book "Three-dimensional geometry and topology" I am a mathematics student who want to read the book Three-dimensional geometry and topology written by William P. Thurston. But I am wondering whether I had enough background for this book or not. About my background, beside the undergraduate mathematics courses, I have taken several advanced courses: Abstract Algebra, Topology, Analysis on Manifold. I also read the following books:

*

*Abstract Algebra by David S. Dummit and Richard M. Foote.

*Topology by James Munkres.

*Analysis on Manifolds by James Munkres.

*Introduction to Smooth Manifolds by John M.Lee.

Do I need something else in order to read and understand this book ? If yes, can you please recommend me some other textbooks (and the order to read it) before start reading this book ?
 A: My suggestion is not to use Thurston's book as the first introductory textbook for the subject.
Try
Schultens, Jennifer, Introduction to 3-manifolds, Graduate Studies in Mathematics 151. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1020-9/hbk). x, 286 p. (2014). ZBL1295.57001.
It is sufficiently gentle and you have the right prerequisites. You can also supplement it with freely available:
A. Hatcher. Notes on Basic 3-Manifold Topology.  https://pi.math.cornell.edu/~hatcher/3M/3Mdownloads.html
For more in-depth treatment, I would suggest
Hempel, John, 3-manifolds, Annals of Mathematics Studies, 86. Princeton, New Jersey: Princeton University Press and University of Tokyo Press. XII, 195 p. hbk: $ 17.00; pbk: $ 6.25 (1976). ZBL0345.57001.."
If you decide to read Thurston's book, I suggest you first read an introductory Riemannian Geometry textbook; my personal preference is do Carmo's "Riemannian Geometry" (at least the first four chapters). Namely, you need to know definitions of Riemannian metrics, connections and curvature.
But there are many nice alternatives, such as Jack Lee's "Introduction to Riemannian Manifolds" book.
Also take a look here for Hatcher's list of suggestions for geometric topology books.
