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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.

References

Blackburn, van Benthem, Wolter, Handbook of modal logic, Elsevier, 2007. For special chapters and their authors see below in “Contributors.

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.