In music theory, counterpoint is the relationship of two or more simultaneous musical lines (also called voices) that are harmonically dependent on each other, yet independent in rhythm and melodic contour. The term originates from the Latin punctus contra punctum meaning "point against point", i.e. "note against note".

John Rahn describes counterpoint as follows:

It is hard to write a beautiful song. It is harder to write several individually beautiful songs that, when sung simultaneously, sound as a more beautiful polyphonic whole. The internal structures that create each of the voices separately must contribute to the emergent structure of the polyphony, which in turn must reinforce and comment on the structures of the individual voices. The way that is accomplished in detail is ... 'counterpoint'.

Counterpoint has been most commonly identified in the European classical tradition, strongly developing during the Renaissance and in much of the common practice period, especially in the Baroque period. In Western pedagogy, counterpoint is taught through a system of species (see below).

There are several different forms of counterpoint, including imitative counterpoint and free counterpoint. Imitative counterpoint involves the repetition of a main melodic idea across different vocal parts, with or without variation. Compositions written in free counterpoint often incorporate non-traditional harmonies and chords, chromaticism and dissonance.

The term "counterpoint" has been used to designate a voice or even an entire composition. Counterpoint focuses on melodic interaction—only secondarily on the harmonies produced by that interaction.

Work initiated by Guerino Mazzola (born 1947) has given counterpoint theory a mathematical foundation. In particular, Mazzola's model gives a structural (and not psychological) foundation of forbidden parallels of fifths and the dissonant fourth. Octavio Agustin has extended the model to microtonal contexts. Another theorist who has tried to incorporate mathematical principles in his study of counterpoint is Sergei Taneyev (1856–1915). Inspired by Spinoza, Taneyev developed a theory which covers and generalizes a wide range of advanced contrapuntal phenomena, including what is known to the English-speaking theorists as invertible counterpoint (although he describes them mainly using his own, custom-built terminology), by means of linking them to simple algebraic procedures.

In counterpoint, the functional independence of voices is the prime concern. The violation of this principle leads to special effects, which are avoided in counterpoint. In organ registers, certain interval combinations and chords are activated by a single key so that playing a melody results in parallel voice leading. These voices, losing independence, are fused into one and the parallel chords are perceived as single tones with a new timbre. In counterpoint, parallel voices are prohibited because they violate the heterogeneity of musical texture when independent voices occasionally disappear turning into a new timbre quality and vice versa.