  Following the classical approach of Birkhoff, we suggest an enriched version
of enriched universal algebra. Given a suitable base of enrichment $\mathcal
V$, we define a language $\mathbb L$ to be a collection of $(X,Y)$-ary function
symbols whose arities are taken among the objects of $\mathcal V$. The class of
$\mathbb L$-terms is constructed recursively from the symbols of $\mathbb L$,
the morphisms in $\mathcal V$, and by incorporating the monoidal structure of
$\mathcal V$. Then, $\mathbb L$-structures and interpretations of terms are
defined, leading to enriched equational theories. In this framework we
characterize algebras for finitary monads on $\mathcal V$ as models of an
equational theories.
