Max, also known as Max/MSP/Jitter, is a visual programming language for music and multimedia developed and maintained by San Francisco-based software company Cycling '74. Over its more than thirty-year history, it has been used by composers, performers, software designers, researchers, and artists to create recordings, performances, and installations.

The Max program is modular, with most routines existing as shared libraries. An application programming interface (API) allows third-party development of new routines (named external objects). Thus, Max has a large user base of programmers unaffiliated with Cycling '74 who enhance the software with commercial and non-commercial extensions to the program. Because of this extensible design, which simultaneously represents both the program's structure and its graphical user interface (GUI), Max has been described as the lingua franca for developing interactive music performance software.

Miller Puckette began work on Max in 1985, at the Institut de Recherche et Coordination Acoustique/Musique (IRCAM) in Paris. Originally called The Patcher, this first version provided composers with a graphical interface for creating interactive computer music scores on the Macintosh. At this point in its development Max couldn't perform its own real-time sound synthesis in software, but instead sent control messages to external hardware synthesizers and samplers using MIDI or a similar protocol. Its earliest widely recognized use in composition was for Pluton, a 1988 piano and computer piece by Philippe Manoury; the software synchronized a computer to a piano and controlled a Sogitec 4X for audio processing.

In 1989, IRCAM developed Max/FTS ("Faster Than Sound"), a version of Max ported to the IRCAM Signal Processing Workstation (ISPW) for the NeXT. Also known as "Audio Max", it would prove a forerunner to Max's MSP audio extensions, adding the ability to do real-time synthesis using an internal hardware digital signal processor (DSP) board. In 1989, IRCAM worked with Joel Chadabe and Ben Austin of Intelligent Computer Music Systems to license the software for commercial sales in the United States. With the 1990 bankruptcy of Intelligent Computer Music Systems, both the Max Software and Ben Austin moved to Opcode Systems, which became the publisher of record for Max.

Although Opcode launched its commercial version named Max in 1990, developed and extended by David Zicarelli, the product was becoming a poor fit for Opcode, which was squarely towards commercial music production. Thus Zicarelli in 1997 acquired the publishing rights and founded a new company, Cycling '74, to continue commercial development. The timing was fortunate, as Opcode was acquired by Gibson Guitar in 1998 and ended operations in 1999.

IRCAM's in-house Max development was also winding down; the last version produced there was jMax, a direct descendant of Max/FTS developed in 1998 for Silicon Graphics (SGI) and later for Linux systems. It used Java for its graphical interface and C for its real-time backend, and was eventually released as open-source software.

Meanwhile, Puckette had independently released a fully redesigned open-source composition tool named Pure Data (Pd) in 1996, which, despite some underlying engineering differences from the IRCAM versions, continued in the same tradition. Cycling '74's first Max release, in 1997, was derived partly from Puckette's work on Pure Data. Called Max/MSP ("Max Signal Processing", or the initials Miller Smith Puckette), it remains the most notable of Max's many extensions and incarnations: it made Max capable of manipulating real-time digital audio signals without dedicated DSP hardware. This meant that composers could now create their own complex synthesizers and effects processors using only a general-purpose computer like the Macintosh PowerBook G3.

In 1999, the Netochka Nezvanova collective released NATO.0+55+3d, a suite of externals that added extensive real-time video control to Max.