I want to study anabelian geometry, but unfortunately I'm having difficulties in finding some materials about it. If you could offer me some books/papers/articles I would be glad.

9$\begingroup$ Szamuely, Galois Groups and Fundamental Groups, Cambridge Studies in Advanced Mathematics, vol. 117, Cambridge University Press, 2009. $\endgroup$– Felipe VolochCommented Oct 4, 2012 at 22:11

8$\begingroup$ The book mentioned by Felipe is available here: math.uchicago.edu/~aanders/books/… $\endgroup$– Mahdi MajidiZolbaninCommented Oct 4, 2012 at 23:25

4$\begingroup$ I don't recommend that book. There are lots of errors (even concerning basic definitions) and inconsistencies. $\endgroup$– Martin BrandenburgCommented Jan 7, 2013 at 11:20

$\begingroup$ (apologies for the overlong link but...) just discovered a recent master's thesis on monoanabelian geometry: google.com/… $\endgroup$– Samantha YCommented Jan 23, 2018 at 17:35
5 Answers
There is this very beautiful survey
Nakamura, Hiroaki; Tamagawa, Akio; Mochizuki, Shinichi
The Grothendieck conjecture on the fundamental groups of algebraic curves
http://www.math.sci.osakau.ac.jp/~nakamura/zoo/rhino/NTM300.pdf
You could also have a look at
Szamuely, Tamás
Heidelberg Lectures on Fundamental Groups

2$\begingroup$ That is quite a list of authors. $\endgroup$ Commented Oct 5, 2012 at 18:39
Jakob Stix, Rational Points and Arithmetic of Fundamental Groups Evidence for the Section Conjecture Springer Lecture Notes in Mathematics 2054, xx+pp.247, Springer 2012. http://www.springer.com/mathematics/algebra/book/9783642306730

2$\begingroup$ I'm sure this book will be the one to get, once it comes out. If you start with Szamuely as an introduction, you could then move on to this afterwards. $\endgroup$ Commented Oct 5, 2012 at 13:01

$\begingroup$ springer.com/mathematics/numbers/book/9783642239045 Is this the same book? $\endgroup$ Commented Oct 5, 2012 at 14:22

$\begingroup$ No (it is a collection of conference talks), but this is also a good source. $\endgroup$– user19475Commented Oct 5, 2012 at 14:25
This volume, Galois Groups and Fundamental Groups, edited by Leila Schneps has a great collection of articles, as does this volume, Geometric Galois Actions, including a nice article by Florian Pop on "Glimpses of Grothendieck's anabelian geometry."
If you'd like videos, here is a series of lectures on related topics, including a long series by Pop on anabelian geometry. At MSRI, you can find some lectures from Fall 1999, including one specifically about anabelian geometry.
Florian Pop, Lectures on Anabelian phenomena in geometry and arithmetic (pdf)
Yuri Tschinkel, Introduction to anabelian geometry, talk at Symmetries and correspondences in number theory, geometry, algebra, physics: intradisciplinary trends, Oxford 2014 (slides pdf)
The article
Matsumoto, Makoto, Arithmetic fundamental groups and moduli of curves. School on Algebraic Geometry (Trieste, 1999), 355–383, ICTP Lect. Notes, 1, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2000.
has a nice concrete discussion of fundamental groups.

1$\begingroup$ users.ictp.it/~pub_off/lectures/lns001/Matsumoto/Matsumoto.pdf $\endgroup$ Commented May 7, 2013 at 23:11