This book provides a gentle introduction to category theory oriented to software engineering. Assuming only a minimum of mathematical background, this book explores the use of categorical constructions from the point of view of the methods and techniques that have been proposed for the engineering of complex software systems: object-oriented development, software architectures, logical and algebraic specification techniques, models of concurrency, inter alia. After two parts in which basic and more advanced categorical concepts and techniques are introduced, the book illustrates their application to the semantics of CommUnity ? a language for the architectural design of interactive systems.