  We develop a new general framework for algebras and clones, called Universal
Clone Algebra. Algebras and clones of finitary operations are to Universal
Algebra what t-algebras and clone algebras are to Universal Clone Algebra.
Clone algebras have been recently introduced to found a one-sorted, purely
algebraic theory of clones, while t-algebras are first introduced in this
article. We present a method to codify algebras and clones into t-algebras and
clone algebras, respectively. We provide concrete examples showing that general
results in Universal Clone Algebra, when translated in terms of algebras and
clones, give more powerful versions of known theorems in Universal Algebra. We
apply this methodology to Birkhoff's HSP theorem and to the recent topological
versions of Birkhoff's theorem.
