1. to take on (for taking on a shape or character trait, NOT for tasks.)
2. to accept (For any kinds of offer. Gifts, invitations and apologies are the most common things, but it also works for fate. )
Opposite (closest): ablehnen
3. to assume (a theory), to suppose (The idea is that you "accept" a theory as reality. Another way to express it is with "davon ausgehen" )