  In this expository article, we give a self-contained introduction to the
wonderfully well-behaved class of pseudocompact algebras, focusing on the
foundational classes of semisimple and separable algebras. We give
characterizations of such algebras analogous to those for finite dimensional
algebras. We give a self-contained proof of the Wedderburn-Malcev Theorem for
pseudocompact algebras.
