Generalized Pascal triangles (GPT) are constructed top-down
from finite algebras $\algA$ and words $w\in\AAA^+$
similarly as the classical Pascal triangle is constructed
from $\str{\NN;+,0}$ and the constant $1$. A GPT will be
called reversible if it also can be locally constructed
bottom-up, using a binary operation. An algebra will be
called reversible if all its GPT are reversible. Several
kinds of reversibility are introduced and some constructions
of reversible algebras are presented. Reversible algebras
are constructed from algebras satisfying cancellation laws,
or from other reversible algebras. A relationship to
reversibility of cellular automata is briefly discussed.
