This text provides an account of real-time systems: program structures for real-time timing analysis using scheduling theory and specification and verification in different frameworks. The presentation makes use of recent research which has demonstrated the effectiveness and applicability of mathematically-based methods for real-time system design. Each chapter focuses on a particular technique and examples help reinforce the theory presented in the text. Coverage includes advanced scheduling theory, as well as new specification and verification methods, linked together by consideration of a common, non-trivial example. All chapters contains exercises in the general text as well as graded exercises at the end.