Rudiments of Ramsey Theory by Ronald Graham and Steve Butler

Ramsey Theory by Ronald Graham, Bruce Rothchild, Joel Spencer HERE

Ramsey Theory on the Integers by Bruce Landman and Aaron Robertson HERE

Ramsey Theory for Discrete Structures by Hans Jurgen Promel

An intro to RT: Fast Functions, Infinity, and Metamathatics by M. Katz and J. Reimann

Comb. Set Theory: Partition Relations for Cardinals by Erdos, Hajnal, Mate, Rado

Comb. Games: Tic-Tac-Toe by Beck HERE

Aspects of Combinatorics and Combinatorial NT by Sukumar Adhikari (about 2/3 Ramsey)

Fundmentals of Ramsey Theory by Aaron Robertson (second edition of Landman-Robertson?)

Basics of Ramsey Theory by Jungic

Notes on Ramsey Theory (unpublished) by Jungic HERE

Ramsey Theory by Taylor (unpulished) HERE

Variations on a theorem by VDW by Johannson (unpublished) HERE

Combinatorial NT: Results of Hilbert, Schur, Folkman, and Hindman (unpublished) HERE

Collections of Articles that Mostly Use Combinatorics

Mathematics of Ramsey Theory Edited by Jaroslave Nesetril and Vojtech Rodl HERE

Ramsey Theory: Yesterday, Today, and Tommorow edited by Alexander Soifer HERE

Ramsey Theory Books That Use Non-Combinatorial Methods

Nonstandard Methods in RT and Comb NT by Nasso, Goldbring, Lupini. (1/5 Ramsey) HERE

Introduction to Ramsey Spaces by Stevo Todorcevic HERE

Ramsey Theory on Product Spaces by Kanellopoulos HERE

Canonical Ramsey Theory on Polish Spaces by Kanovei, Sabok, Zapletal HERE

Books That Have Some Ramsey In Them

Additive Combinatorics by Terrence Tao and Van Vu (about 1/5 Ramsey) HERE

The Mathematical Coloring Book by Alexander Soifer (about 1/2 Ramsey) HERE

Handbook of Combinatorics edited by Graham, Grotschel, Lovasz. Volume 2 has a chapter on Ramsey Theory

Essays on Numbers and Figures by Viktor Prasolov. 1 chapter on VDW-GW. HERE

Connections in DM: A Celebration of the work of Ron Graham. Edited by Butler, Cooper, Hurlbert. 3 out of 20 chaps on RT.

The Scholar and the State: In Search of VDW by Soifer. A History book. 4 of the 43 chaps on RT.

Comb Mathematics and its Apps edited by Bose and Dowling. 1 chap on kth residue prob.

Slicing the Truth: On the comp. and rev. math. of comb. principles by Hirschfeldt. Logic.

Mathematical Plums edited by Ross Honsberger. 1 chap is on many triangles.

Mathematical Gems edited by Ross Honsberger. 1 chap has a problem on grid coloring.