Key problems and conjectures have significantly advanced Ramsey theory, a field that has seen remarkable progress in the past two decades, with many longstanding issues resolved and new ones emerging. This book serves as a comprehensive resource for those interested in exploring intriguing problems in Ramsey theory, understanding their interconnections, and delving into them more deeply. It is the first of its kind to cover such a wide range of topics within this area. The book presents numerous unsolved problems, conjectures, and related partial results across various domains, including extremal graph theory, additive number theory, discrete geometry, functional analysis, and algorithm design. While most problems are accessible and easy to grasp, they can pose significant challenges in terms of solutions. The content is suitable for a diverse audience, from undergraduate mathematics students to seasoned researchers. This collection is an essential reference for mathematicians focused on combinatorics and number theory, as well as computer scientists engaged in algorithm studies. Topics covered include definitions and notations, classical Ramsey numbers, Paley graphs, multicolor Ramsey numbers, the Erdős–Hajnal conjecture, and various Ramsey-type problems in graph theory and additive number theory.
