This book is an introduction to modal logic, more precisely, to classically based propositional modal logic. There are few books on this subject and even fewer books worth looking at. None of these give an acceptable mathematically correct account of the subject. This book is a first attempt to fill that gap.

Apart from its mathematical clarity, some other features of the book are:

• The central concept of the book is that of a labelled transition structure, and polymodal languages are used from the beginning.

• Modal languages are viewed as a tool for analysing the properties of transition structures, not the other way round.

• There is not an overemphasis on syntactic (proof theoretic) matters.

• Nevertheless, a detailed explanation is given of the differences between the weak completeness and Kripke completeness of formal systems.

• Correspondence properties (the expressibility properties of modal languages) are stressed as an important tool.

• Bisimulations are used as a method of comparing transition structures.

• Each chapter has a decent selection of exercises and over one sixth of the book consists of a comprehensive set of solutions to these exercises.

The book is aimed primarily at a computer science readership. However there is no computer science in the book and very little material which is directly attributable to a computer science motivation. Thus the reader of the book may be interested in modal logic in its own right or because of one or several of its applications in computer science.