This is a survey of the origins of mathematical semantics for modal logics, and its development over the last century or so. It focuses on the algebraic semantics using Boolean algebras with operators and the relational semantics using structures often called Kripke models.

Chapter 1: Introduction

Chapter 2: Beginnings
MacColl's algebraic analysis of modalised statements. C. I. Lewis's systems S1 - S5. Godel's work on provability as a modality.

Chapter 3: Modal Algebras
McKinsey's algebraic construction for the finite model property. Topological models of S4. Jonsson and Tarski's theory of Boolean algebras with operators. Could Tarski have invented Kripke semantics?

Chapter 4: Relational Semantics
Kripke's relatively possible worlds. So who invented relational models? The ideas of Carnap, Bayart, Meredith, Prior, Geach, Kanger, Montague and Hintikka. The place of Kripke.

Chapter 5: The Post-Kripkean Boom of theSixties
The Lemmon-Scott collaboration. Bull's tense algebra, Segerberg's Essay.

Chapter 6: Metatheory of the Seventies and Beyond
Incompleteness, decidability and complexity, first-order-definability, reduction of second-order logic to propositional modal logic, duality, canonicity.

Chapter 7: Some Mathematical Modalities
Dynamic logic of programs, Hennessy-Milner logic, temporal logic of concurrency, the modal mu-calculus, Solovay on provability in arithmetic as a modality, Grothendieck topology as intuitionistic modality, Modal Logic for Coalgebras.