The Allen and Greenough is still under construction;
so some links may not work quite the way you would expect.
320. The proper function of Adverbs, as petrified
case-forms, is to modify Verbs: as, - celenter
ire, to go with speed. It is from this use that they derive
their name (adverbium, from ad, to, and verbum, verb; see §241. b). They also modify adjectives,
showing in what manner or degree the quality described is manifested: as,
splendide mendax, gloriously false.
More rarely they modify othsr adverbs: as, nimis
graviter, too severely. Many adverbs, especially relative
adverbs, serve as connectives, and are hardly to be distinguished from
conjunctions (see §20. g. N.).[For
the derivation and classification of adverbs, see §§214 - 217.]