Arithmetic Ramsey Theory

This book provides a gentle introduction to the fundamental results of Arithmetic Ramsey Theory and some relevant topics in number combinatorics, based on the ultrafilter method, a powerful tool that often simplifies complex proofs and clarifies intricate results. The material presented includes all the classical results in this area, including Ramsey's, Rado's, Hindman's, van der Waerden's, and Hales-Jewett's theorems.