What is complexity theory - and why is it so central to computer science? Complexity theory studies how much time, memory, or other resources are needed to solve algorithmic problems. It provides the foundation for understanding what computers can achieve - and what remains fundamentally beyond reach, even with the best algorithms. From the classical classes P and NP, through reductions, NP-completeness, and approximation problems, to interactive proof systems, PCP theory, and communication complexity, this book gradually introduces the key concepts of theoretical computer science. Lucien Sina not only explains the theory but also conveys the underlying ideas and intuitions. Numerous examples, proofs, and exercises with solutions help deepen understanding and develop a sense of the limits of what can be efficiently computed. The book is ideal for computer science students, instructors, researchers, and anyone seeking a solid yet clearly understandable introduction to complexity theory. It complements the author's other works - "Algorithms and Data Structures", "Theory of Computation", "Logic: Foundations, the P vs. NP Problem, and Information-Theoretic Perspectives", and "Object-Oriented Programming in Java" - forming a coherent series for learning and reference, spanning from fundamental research to practical programming. Complexity theory demonstrates how deeply theory and practice in computer science are intertwined - and why knowing the limits of what is possible is often the first step toward expanding them creatively.