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The Janos Bolyai Mathematical Society and the HUN-REN Alfred Renyi Institute of Mathematics (Budapest, Hungary) organized a week-long conference on the occasion of the 70th birthdays of four excellent mathematicians: Peter Frankl, Zoltan Fueredi, Ervin Gyori and Janos Pach in July 2024. The present volume mainly contains survey papers written by the invited speakers of this conference and it also includes some interesting new results, see, for example, Noga Alon's paper in the area of extremal combinatorics. The book also comprises three excellent surveys written by Hurlbert, Kupavskii, and Jian Wang which give a good overview of extremal set theory. Moreover, two papers written by Balko and Verstraete are surveys of certain sub-branches of Ramsey theory, while two papers written by Aslanyan-Sahakyan and Ihringer present a broad picture of the combinatorial properties of Boolean functions. Likewise, the paper written by Geza Toth covers an interesting area of combinatorial geometry and in addition, there are subsequent papers presenting results on graph theory.

This volume will be a valuable resource for graduate students and young (perhaps also not so young) researchers interested in extremal combinatorics and combinatorial geometry.