To indicate the different execution speeds of a music text you can use following terms:
grave, very slow, slow, adagio, andante, moderately slow, moderately, rather fast, fast, quite fast, quick, very fast.
There exist further terms that, associated to the above-mentioned ones, define more precisely the tempo of the music text. They are:
grave, sustained, imposing, military, grand, scherzo, comic, resolute, passionate, impetuous, sweet, calm, with fire, dying, funereal, chantable, excited, marked, gracious
and so on.
To vary the speed of the movement during its execution you use following terms (their abbreviations are indicated in brackets):
accelerando (acc) (quickening), ritardando (rit) (slowing down), rallentando (rall) (slowing down), piĆ¹ mosso (more motion), lively, strict, smorzando, ritenuto (sudden slowing down).
The agogic can be accompanied by metronomical indications further specifying the tempo too.