Foreword by Angelika Steger.- Preface.- Conventions.- Part I Roots of Ramsey Theory: 1.1 Ramsey’s theorem.- 1.2 From Hilbert’s cube lemma to Rado’s thesis.- Part II A Starting Point of Ramsey Theory: Parameter Sets: 2.1 Definitions and basic examples.- 2.2 Hales-Jewett’s theorem.- 2.3 Graham-Rothschild’s theorem.- 2.4 Canonical partitions.- Part III Back to the Roots: Sets: 3.1 Ramsey numbers.- 3.2 Rapidly growing Ramsey functions.- 3.3 Product theorems.- 3.4 A quasi Ramsey theorem.- 3.5 Partition relations for cardinal numbers.- Part IV Graphs and Hypergraphs: 4.1 Finite graphs.- 4.2 Infinite graphs.- 4.3 Hypergraphs on parameter sets.- 4.4. Ramsey statements for random graphs.- 4.5 Sparse Ramsey Theorems.- Part V Density Ramsey Theorems: 5.1 Szemerédi’s Theorem.- 5.2 Density Hales-Jewett Theorem.- 5.3 Proof of the density Hales-Jewett theorem.- References.- Index.

This monograph covers the most important developments in Ramsey theory from its beginning in the early 20th century via its many breakthroughs and highlights in the late 20th century up to recent important developments in the early 21st century.