Algorithmic Problems & Their Complexity -- Fundamental Complexity Classes -- Reductions — Algorithmic Relationships Between Problems -- The Theory of NP-Completeness -- NP-complete and NP-equivalent Problems -- The Complexity Analysis of Problems -- The Complexity of Approximation Problems — Classical Results -- The Complexity of Black Box Problems -- Additional Complexity Classes and Relationships Between Complexity Classes -- Interactive Proofs -- The PCP Theorem and the Complexity of Approximation Problems -- Further Topics From Classical Complexity Theory -- The Complexity of Non-uniform Problems -- Communication Complexity -- The Complexity of Boolean Functions.Complexity theory is the theory of determining the necessary resources for the solution of algorithmic problems and, therefore, the limits of what is possible with the available resources. An understanding of these limits prevents the search for non-existing efficient algorithms. This textbook considers randomization as a key concept and emphasizes the interplay between theory and practice: New branches of complexity theory continue to arise in response to new algorithmic concepts, and its results - such as the theory of NP-completeness - have influenced the development of all areas of computer science. The topics selected have implications for concrete applications, and the significance of complexity theory for today's computer science is stressed throughout.