RESUMEN

It is well known that 2-D TQFTs are equivalent to Frobenius algebras. This correspondence is realized via cobordism. This construction is summarized by the category 2Cob which admits a completely algebraic description as the free symmetric monoidal category on a conmmutative Frobenious algebra. We will review these facts aided by as many diagrams and graphs as possible. We will also compare this construction with the more recent one of the category 2Thick, whose objects and morphisms can be thought of as open strings and diffeomorphim classes of planar open string worldsheets. We will show how 2thick is a free monoidal category on a non-conmmutative Frobenious algebra. This way we justify the choice of data in the Moore-Segal axioms for an OC-TFT (open-closed topological field theory). We will try to make all the correspondences as clear as possible to introduce the audience to knot invariants (via 2Cob and Khovanov's homology) and invariants of 3-dimensional membranes (via 2Thick and a suitable "topological membrane theory").