This chapter sets out several basic ideas of what I will refer to as the autosegmental–metrical (AM) theory of intonational phonology. The somewhat cumbersome name reflects the intellectual heritage of the theory in American non-linear ‘autosegmental’ and ‘metrical’ phonology of the 1970s, but it also embodies certain ideas about intonational structure that I will develop in chapters 7 and 8. The general approach has its origins in three influential PhD theses, namely Liberman (1975), Bruce (1977), and – especially – Pierrehumbert (1980). During the 1980s the theory was applied to a variety of European languages (e.g. Ladd 1983a; Gussenhoven 1984) and served as the basis of a number of systems for synthesising intonation by rule (e.g. Pierrehumbert 1981; Anderson, Pierrehumbert, and Liberman 1984; Ladd 1987b). It was central in the development of ‘laboratory phonology’ (Beckman and Kingston 1990; Pierrehumbert, Beckman and Ladd 2000), in that it very early adopted the goal of explaining details of instrumentally measured F0in a phonological description; it takes for granted that instrumental phonetics is a source of data for phonological theory. Since the early 1990s, it has given rise to a whole series of ToBI (Tone and Break Index) transcription systems for the intonation of a variety of languages, and on this basis it is widely presupposed in discussions of prosodic structure and of the relation between intonation and information structure.