Slow tempo

largo – broadly (40–60 bpm)
lento – slowly (40–60 bpm)
adagio – slow and stately (literally, “at ease”) (66–76 bpm)
grave – slow and solemn (20–40 bpm)

Moderate tempo

andante – at a walking pace (76–108 bpm)
andantino – slightly faster than andante
moderato – moderately (108–120 bpm)
sostenuto – sustained, prolonged
allegretto – moderately fast (but less so than allegro)
allegro moderato – moderately quick (112–124 bpm)

Fast tempo

allegro – fast, quickly and bright (120–168 bpm)
vivo, vivace – lively and fast (≈140 bpm)
presto – very fast (168–200 bpm)
prestissimo – extremely fast (more than 200bpm)

Additional terms‎

molto – much
assai – very much
con moto – with motion
commodo – comfortably
non troppo – not too much, allegro non troppo (fast, but not too much)
non tanto – not so much
sempre – all time
meno mosso – less movement or slower
più mosso – more movement or faster

For expressive

ritenuto – slightly slower
ritardando – slowing down gradually
allargando – growing broader
rallentando – gradual slowing down
accelerando, stringendo – speeding up
animando – animating
stretto – in faster tempo, often near the conclusion of a section

Return to previous speed

a tempo – returns to the base tempo after an adjustment
tempo primo, tempo I – denotes an immediate return to the piece’s original base tempo after a section in a different tempo
l’istesso tempo – at the same speed