In the modern world, the importance of information can hardly be overestimated. Information also plays a prominent role in scientific computations. A branch of computational complexity which deals with problems for which information is partial, noisy and priced is called informationbased complexity.

In a number of information-based complexity books, the emphasis was on partial and exact information. In the present book, the emphasis is on noisy information. We consider deterministic and random noise. The analysis of noisy information leads to a variety of interesting new algorithms and complexity results.

The book presents a theory of computational complexity of continuous problems with noisy information. A number of applications is also given. It is based on results of many researchers in this area (including the results of the author) as well as new results not published elsewhere.

This work would not have been completed if I had not received support from many people. My special thanks go to H. Woźniakowski who encouraged me to write such a book and was always ready to offer his help. I appreciate the considerable help of J.F. Traub. I would also like to thank M. Kon, A. Werschulz, E. Novak, K. Ritter and other colleagues for their valuable comments on various portions of the manuscript.

I wish to express my thanks to the Institute of Applied Mathematics and Mechanics at the University of Warsaw, where the book was almost entirely written.