As Knuth himself says, it is impossible for any one person to keep up with all the research in computer science, but these 3 volumes do a remarkably good job of distilling the most important results and explaining them with mathematical rigor.

Each volume contains 2 chapters. Ch. 1, Basic Concepts: mathematical foundations and a description of MIX, a hypothetical machine (now available in software emulations). Ch. 2, Information Structures: lists, trees, memory allocation, garbage collection. Ch. 3, Random Numbers: how to produce series of "random" numbers and test their statistical properties. Ch. 4, Arithmetic: algorithms for integer and floating-point arithmetic. Ch. 5, Sorting: both in memory and on disks or tapes. Ch. 6, Searching: sequential, binary, hashing.

Despite the detailed coverage of the topics, which often involves esoteric mathematical notation, the author's lively style makes the algorithms and the main theoretical results relatively easy to grasp. If all you care about is getting a program to run, buy another book; but if you really want to understand how and why software works, there's nothing quite like this.