Algorithmic Randomness and Complexity (Theory and Applications of Computability)

From the reviews:

Develops the prerequisites to algorithmic randomness: computability theory and Kolmogorov complexity. ... Studying these ... one should be able to proceed in the area with confidence. A draft of the book under review has been circulating for years and the reviewer found it to be the best source when attempting to conduct research in the area ... . It is advantageous for the future of the area of algorithmic randomness that these two books were published at the cusp of a period of great activity. (Bjorn Kjos-Hanssen, Mathematical Reviews, Issue 2012 g)

A thorough and systematic study of algorithmic randomness, this long-awaited work is an irreplaceable source of well-presented classic and new results for advanced undergraduate and graduate students, as well as researchers in the field and related areas. The book joins a select number of books in this category. (Hector Zenil, ACM Computing Reviews, October, 2011)