A self-dual Lie or associative algebra is one which is isomorphic as a module its dual. Its cohomology with coefficients in itself is then isomorphic to its cohomology with coefficients in the dual; a quasi-self dual algebra is one possessing the latter property. In the category of such algebras cohomology with coefficients in itself (which controls deformations) becomes a contravariant functor. of the category of the category of associative or Lie algebras, respectively. Finite dimensional associative self-dual algebras over a field are identical with symmetric Frobenius algebras (which are closely connected to 1+1 dimensional topological quantum field theory). Finite poset algebras are quasi self-dual.