TITLE: Good way to learn Ramsey Theory
QUESTION [14 upvotes]: What are some good books on Ramsey theory? I have Van Lint's book on Combinatorics: is this enough preparation to start reading about Ramsey theory? I want a book that includes important results and has good proofs.

REPLY [14 votes]: This is a list of some resource material on Ramsey Theory:

Expository note on Arithmetic Ramsey theory by Terence Tao. This contains the basic theorems and proofs presented in a very nice manner.

Ramsey Theory by R.L. Graham, B.L. Rothschild, and J. Spencer is a book which contains an introduction to nearly all areas in finite Ramsey theory. It contains proofs of all the basic results: Ramsey's theorem, van der Waerden theorem, Hales Jewett theorem, Schur's theorem, Rado's theorem, Graham's theorem etc.

Ramsey theory on the integers by Landman is a book accessible to undergraduates. It is unique in the sense that it uses only elementary mathematics and describes many research problems. Most of the book deals with variants of the van der Waerden's theorem.

Mathematics of Ramsey theory by Nesteril & Rodl is a book which I haven't read but is supposed to contain many advanced techniques.

The ebook Introduction to Graph Ramsey Theory by Yusheng Li and
Wenan Zang available here.

Elemental methods in Ergodic Ramsey theory by McCutcheon introduces one of the current approaches to Ramsey theory (via Ergodic theory). I have only read the first chapter but it seems an accessible and well written book.

Erdos' book Partition Relations for Cardinals (Infinite Ramsey theory). I haven't read it.