CafeOBJ is an industrial strength modern algebraic specification language, a successor of the famous OBJ language, and directly incorporating new paradigms such as behavioural concurrent specification and rewriting logic. CafeOBJ is the core of an environment supporting the systems (mainly software but not only) development process at several levels, including prototyping, specification, and formal verification.This book presents not only the formal definition of the language and its semantics, but also methodologies for specification and verification in CafeOBJ, with emphasis on concurrent object composition and modularity.The presentation of the CafeOBJ concepts is supported by many examples, and an appendix illustrates the power of the language and its methodologies by a larger CASE study including specification, testing, and verification.The book may be used both by software engineers interested in algebraic methodologies, and by students and researchers in software engineering and/or theoretical computing science as a fast introduction to state-of-art algebraic specification.