The Art of Computer Programming, usually abbreviated TAOCP, is Donald Knuth’s landmark series on algorithms and the mathematics used to analyze them. Knuth began the project in the early 1960s; the first volume, Fundamental Algorithms, appeared in 1968. The work was originally planned as a single book and grew into a multi-volume series that Knuth is still extending.
The published volumes cover a broad sweep of the field. Volume 1 treats fundamental algorithms and basic data structures, Volume 2 covers seminumerical algorithms, and Volume 3, Sorting and Searching, is a deep study of those two core problems. Later volumes, 4A and 4B, address combinatorial algorithms, with further parts and a planned Volume 5 still in progress and appearing as fascicles.
What set TAOCP apart was its insistence on mathematical rigor. Rather than simply presenting code, Knuth analyzes each algorithm to determine precisely how much time and space it uses, deriving exact formulas rather than rough impressions. This made the analysis of algorithms a serious quantitative discipline.
The series is widely regarded as one of the great works of science. Knuth’s own page records that at the end of 1999 the books were named among the best twelve physical-science monographs of the century by American Scientist, placing them in the company of Dirac, Einstein, and Feynman. Decades after the first volume, it remains a standard reference for anyone who wants to understand algorithms from the ground up.