This idea [that modal operators perform quantification without making use of explicit variables and binding], when expressed mathematically, has turned out to be the most significant milestone in the history of modal logic.
Blackburn, van Benthem, Wolter, Handbook of modal logic, Elsevier, 2007. For special chapters and their authors see below in “Contributors.
Carnielli, Pizzi, modalities and multimodalities, Springer, 2008
Yde Venema, website: algebraic- and coalgebraic aspects of modal logic. e.g §6 in the "handbook" starting at p.331 in this book without a (global) list of contents.
Blackburn, van Bentham, Modal logic: A semantic perspective, “handbook” §1
Valentin Goranko and Martin Otto. “handbook” §5 Model theory of modal logic.
Bradfield, Stirling, “handbook” §12 Modal -calculi
Sergei Artemov, “handbook” §16 Modal logic in mathematics. modal logics of proof, logics of space and dynamic systems, modal logics in set theory.
Van der Hoek, Pauly, “handbook” §20 Modal logic for games and information. Game theory.