This book presents a fundamental mathematical and logical approach to softΒ ware and systems engineering. Considering the large number of books deΒ scribing mathematical approaches to program development, it is important to explain what we consider to be the specific contribution of our book, to identify our goals, and to characterize our intended target audience. Most books dealing with the mathematics and logics of programming and system development are mainly devoted to programming in the small. This is in contrast to our book where the emphasis is on modular system development with the help of component specifications with precisely identified interfaces and refinement concepts. Our book aims at systems development carried out in a systematic way, based on a clear mathematical theory. We do not claim that this book presents a full-blown engineering method. In fact, this is certainly not a book for the application-driven software engiΒ neer looking for a practical method for system development in an industrial context. It is much rather a book for the computer scientist and the scientifiΒ cally interested engineer who looks for basic principles of system development and, moreover, its mathematical foundations. It is also a book for method builders interested in a proper mathematical foundation on which they can build a practical development method and industrial-strength support tools.