A "theory" is a signature, a set of variables and a set of equational laws. Any theory gives a variety of algebras as follows. Given a theory formula_8, an "algebra" of formula_8 consists of a set formula_10 together with, for each operation formula_3 of formula_8 with arity formula_13, a function formula_14 such that for each axiom formula_7 and each assignment of elements of formula_10 to the variables in that axiom, the equation holds that is given by applying the operations to the elements of formula_10 as indicated by the trees defining formula_5 and formula_6. We call the class of algebras of a given theory formula_8 a "variety of algebras".