TeX (/tɛx/), stylized within the system as TeX, is a typesetting program which was designed and written by computer scientist and Stanford University professor Donald Knuth and first released in 1978. The term now refers to the system of extensions – which includes software programs called TeX engines, sets of TeX macros, and packages which provide extra typesetting functionality – built around the original TeX language. TeX is a popular means of typesetting complex mathematical formulae; it has been noted as one of the most sophisticated digital typographical systems.

TeX is widely used in academia, especially in mathematics, computer science, economics, political science, engineering, linguistics, physics, statistics, and quantitative psychology. It has long since displaced Unix troff (the previously favored formatting system), in most Unix installations (although troff still remains as the default formatter of the UNIX documentation). It is also used for many other typesetting tasks, especially in the form of LaTeX, ConTeXt, and other macro packages.

TeX was designed with two main goals in mind: to allow anybody to produce high-quality books with minimal effort, and to provide a system that would give exactly the same results on all computers, at any point in time (together with the Metafont language for font description and the Computer Modern family of typefaces). TeX is free software, which made it accessible to a wide range of users.

When the first paper volume of Knuth's The Art of Computer Programming was published in 1968, it was typeset using hot metal typesetting on a Monotype machine. This method, dating back to the 19th century, produced a "classic style" appreciated by Knuth. When the second edition was published, in 1976, the whole book had to be typeset again because the Monotype technology had been largely replaced by phototypesetting, and the original fonts were no longer available. When Knuth received the galley proofs of the new book on 30 March 1977, he found them inferior. Disappointed, Knuth set out to design his own typesetting system.

Knuth saw for the first time the output of a high-quality digital typesetting system, and became interested in digital typography. On 13 May 1977, he wrote a memo to himself describing the basic features of TeX. He planned to finish it on his sabbatical in 1978 (though ultimately the language's syntax was not frozen until 1989^{[citation needed]}). Guy Steele happened to be at Stanford during the summer of 1978, when Knuth was developing his first version of TeX. When Steele returned to the Massachusetts Institute of Technology that autumn, he rewrote TeX's input/output (I/O) to run under the Incompatible Timesharing System (ITS) operating system. The first version of TeX, called TeX78, was written in the SAIL programming language to run on a PDP-10 under Stanford's WAITS operating system.

For later versions of TeX, Knuth invented the concept of literate programming, a way of producing compilable source code and cross-linked documentation typeset in TeX from the same original file. The language used is called WEB and produces programs in DEC PDP-10 Pascal.

TeX82, a new version of TeX rewritten from scratch, was published in 1982. Among other changes, the original hyphenation algorithm was replaced by a new algorithm written by Frank Liang. TeX82 also uses fixed-point arithmetic instead of floating-point, to ensure reproducibility of the results across different computer hardware, and includes a real, Turing-complete programming language, following intense lobbying by Guy Steele. In 1989, Donald Knuth released new versions of TeX and Metafont. Despite his desire to keep the program stable, Knuth realized that 128 different characters for the text input were not enough to accommodate foreign languages; the main change in version 3.0 of TeX is thus the ability to work with 8-bit inputs, allowing 256 different characters in the text input. TeX3.0 was released on March 15, 1990.

Since version 3, TeX has used an idiosyncratic version numbering system, where updates have been indicated by adding an extra digit at the end of the decimal, so that the version number asymptotically approaches π. This is a reflection of the fact that TeX is now very stable, and only minor updates are anticipated. The current version of TeX is 3.141592653; it was last updated in 2021. The design was frozen after version 3.0, and no new feature or fundamental change will be added, so all newer versions will contain only bug fixes. Even though Donald Knuth himself has suggested a few areas in which TeX could have been improved, he indicated that he firmly believes that having an unchanged system that will produce the same output now and in the future is more important than introducing new features. For this reason, he has stated that the "absolutely final change (to be made after my death)" will be to change the version number to π, at which point all remaining bugs will become features. Likewise, versions of Metafont after 2.0 asymptotically approach e (currently at 2.7182818), and a similar change will be applied after Knuth's death.