This graduate text explains what computers can and can't accomplish efficiently and the implications for various areas of computer science.

Computational complexity theory is about the fundamental capabilities and limitations of efficient computation. Framing the subject in the broader context of computer science, this guidebook is both a self-contained tutorial for beginning graduate students in all areas of computer science and a thorough reference for specialists. Using only elementary discrete math, the book rigorously covers the central concepts of time, space, and randomness in computing, as well as connections to other areas of computer science such as cryptography and machine learning. Intuitions and general techniques are emphasized. The book features full proofs, numerous concrete examples and illustrations, and hundreds of exercises.