The purpose of this book is to present the fundamental ideas behind operational, denotional and axiomatic semantics; stress their relationship by formulating and proving relevant theorems; and to illustrate the applicability of formal semantics as a tool in computer science. The bulk of the text concentrates on a small core language of while-programs for which the three approaches are developed to roughly the same level of sophistication. To demonstrate the applicability of formal semantics, the authors show how to use semantics for validating prototype implementations of programming languages; how to use semantics for verifying analyses used in more advanced implementations of programming languages; and how to use semantics for verifying useful program properties including information about execution time. The reader should have some experience of functional programming and the BNF-style of specifying the syntax of programming languages.