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Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarskis quest for finding structure in logic leads to cylindriclike algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways: as an algebraic form of definability theory, as a study of higherdimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (cylindric in the name refers to geometric aspects). Cylindriclike algebras have a wide range of applications, in, e.g., natural language theory, database theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the HenkinMonkTarski monographs. It is dedicated to the memory of Leon Henkin.
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