Abstract
Topological Quantum Field Theory(TQFT) is an axiomatic theory of quantum field theory. In this thesis, we start from studying the classical cobordism theory of manifolds, which serves as the basic model for defining general TQFT, and then construct Euler TQFT and finite total homotopy TQFT. Furthermore, we show that there is an one-to-one correspondence between 2D-TQFT and Frobenius algebras.