Short answers, pulled from the story.
A melody is a linear succession of musical tones that a listener perceives as a single entity. In its most literal sense it is a combination of pitch and rhythm, though the essential elements also include duration, timbre, texture, and loudness. It functions as the foreground to the background accompaniment in a musical work.
Kirnberger argued that "the true goal of music, its proper enterprise, is melody," and that all parts of harmony have as their ultimate purpose only beautiful melody. He concluded that harmony is subordinate to melody as a means is subordinate to an end.
Jazz musicians call the main melody the "lead" or "head" and use it as a starting point for improvisation. Rock and folk music typically employ one or two melodies, such as verse and chorus, sometimes with a contrasting bridge. Indian classical music centers entirely on melody and rhythm, with no chord changes or harmonic foundation.
A leitmotif is a motif or melody associated with a specific idea, person, or place, used as a recurring musical symbol. Richard Wagner popularized the concept in western classical music.
Twentieth century composers expanded melody beyond fixed pitch and rhythm patterns by giving structural roles to timbre and texture. Examples include Elliott Carter's Eight Etudes and a Fantasy, which contains a movement with only one pitch, and Ruth Crawford-Seeger's String Quartet 1931, which creates melody through "dissonant dynamics" alone. György Ligeti's Aventures uses recurring phonetics rather than conventional pitch sequences to form its linear structure.
Paul Narveson claimed in 1984 that more than three-quarters of melodic topics had not been explored thoroughly. He and others noted that many existing explanations of melody confine themselves to specific stylistic models and are too exclusive to capture the full range of the concept.