This monograph initiates a theory of new categorical structures that generalize the simplicial
Segal property to higher dimensions. The authors introduce the notion of a d-Segal space which
is a simplicial space satisfying locality conditions related to triangulations of d-dimensional
cyclic polytopes. Focus here is on the 2-dimensional case. Many important constructions are
shown to exhibit the 2-Segal property including Waldhausen's S-construction Hecke-Waldhausen
constructions and configuration spaces of flags. The relevance of 2-Segal spaces in the study
of Hall and Hecke algebras is discussed. Higher Segal Spaces marks the beginning of a program
to systematically study d-Segal spaces in all dimensions d. The elementary formulation of
2-Segal spaces in the opening chapters is accessible to readers with a basic background in
homotopy theory. A chapter on Bousfield localizations provides a transition to the general
theory formulated in terms of combinatorial model categories that features in the main part
of the book. Numerous examples throughout assist readers entering this exciting field to move
toward active research established researchers in the area will appreciate this work as a
reference.
