ad libitum
At the performer's discretion — an instruction allowing freedom in tempo, ornamentation, or inclusion.
In Depth
Ad libitum (often abbreviated ad lib.) gives the performer freedom to deviate from the written score. This might mean adding ornamentation, adjusting the tempo, including or omitting a particular passage, or improvising freely over a given harmonic framework.
In jazz, ad lib. is the default state — improvisation is expected. In classical music, it appears more sparingly, usually in cadenzas or passages where the composer wants the performer to exercise artistic judgment. The opposite instruction is obbligato (obligatory), indicating a part that must be played exactly as written.
In Baroque opera, singers would ad lib. so extensively during da capo repeats that the original melody was sometimes unrecognisable — and audiences loved it.