Considered an expert at writing compilers, Knuth started to write a book about compiler design in 1962, and soon realized that the scope of the book needed to be much larger. In June 1965, Knuth finished the first draft of what was originally planned to be a single volume of twelve chapters. His hand-written manuscript was 3,000 pages long: he had assumed that about five hand-written pages would translate into one printed page, but his publisher said instead that about 1½ hand-written pages translated to one printed page. This meant the book would be approximately 2,000 pages in length. At this point, the plan was changed: the book would be published in seven volumes, each with just one or two chapters. Due to the growth in the material, the plan for Volume 4 has since expanded to include Volumes 4A, 4B, 4C, and possibly 4D.

In 1976, Knuth prepared a second edition of Volume 2, requiring it to be typeset again, but the style of type used in the first edition (called hot type) was no longer available. In 1977, he decided to spend a few months working up something more suitable. Eight years later, he returned with TeX, which is currently used for all volumes.

The famous offer of a reward check worth "one hexadecimal dollar" (100HEX base 16 cents, in decimal, is $2.56) for any errors found, and the correction of these errors in subsequent printings, has contributed to the highly polished and still-authoritative nature of the work, long after its first publication. Another characteristic of the volumes is the variation in the difficulty of the exercises. The level of difficulty ranges from "warm-up" exercises to unsolved research problems, providing a challenge for any reader. Knuth's dedication is also famous:

This series of books is affectionately dedicatedto the Type 650 computer once installed atCase Institute of Technology,in remembrance of many pleasant evenings.[nb 1]

All examples in the books use a language called "MIX assembly language", which runs on the hypothetical MIX computer. (Currently, the MIX computer is being replaced by the MMIX computer, which is a RISC version.) Software such as GNU MDK exists to provide emulation of the MIX architecture.

Some readers are put off by the use of assembly language, but Knuth considers this necessary because algorithms need to be in context in order for their speed and memory usage to be judged. This does, however, limit the accessibility of the book for many readers, and limits its usefulness as a "cookbook" for practicing programmers, who may not be familiar with assembly, or who may have no particular desire to translate assembly language code into a high-level language. A number of more accessible algorithms textbooks using high-level language examples exist and are popular for precisely these reasons.

American Scientist has included this work among "100 or so Books that shaped a Century of Science", referring to the 20th century, and within the computer science community it is regarded as the first and still the best comprehensive treatment of its subject. Covers of the third edition of Volume 1 quote Bill Gates as saying, "If you think you're a really good programmer . . . read (Knuth's) Art of Computer Programming . . . You should definitely send me a résumé if you can read the whole thing." [nb 2] The New York Times referred to it as "the profession's defining treatise".

In order by volume number:

In order by publication date: