  A retract variety is defined as a class of algebras closed under
isomorphisms, retracts and products. Let a principal retract variety be
generated by one algebra and a set-principal retract variety be generated by
some set of algebras. It is shown that (a) not each set-principal retract
variety is principal, and (b) not each retract variety is set-principal. A
class of connected monounary algebras $\mathcal{S}$ such that every retract
variety of monounary algebras is generated by algebras that have all connected
components from $\mathcal{S}$ and at most two connected components are
isomorphic is defined, this generating class is constructively described. All
set-principal retract varieties of monounary algebras are characterized via
degree function of monounary algebras.
