Rudiments of Ramsey Theory Second Edition

Preface to the second edition
In the 35 years since the lectures which form this book were given the area of
Ramsey theory has continued to undergo tremendous growth, particularly in the
last decade. We are taking advantage of this time to revisit these rudiments to fill in
what has happened since the first edition came out. We also are taking advantage
of this time to correct any errors in the first edition of which we were aware.1
The goal of this book, as before, is to serve as an introduction to the field of
Ramsey theory. When this book first appeared it was difficult to find resources
about Ramsey theory. In the last few decades the situation has changed drastically
and further information about the field is now available in several books includ-
ing Ramsey Theory by Graham, Rothschild and Spencer2; Ramsey Theory on the
Integers by Landman and Robertson; Elemental Methods in Ergodic Ramsey The-
ory by McCutcheon; and Ramsey Theory for Discrete Structures by Pr¨omel. In
addition there are several collected volumes dedicated to Ramsey theory, including
Mathematics of Ramsey Theory edited by Neˇsitˇril and R¨odl and Ramsey Theory:
Yesterday, Today, and Tomorrow edited by Soifer, as well as a number of surveys
including [CoFS, GN, JNR, Ne, Rad, Ros, Tro]. We hope that this small work
will still continue to be a helpful guide for those starting out in the field.