These lectures are an introduction to formal semiclassical quantization of classical field theory. First, we develop the Hamiltonian formalism for classical field theories on space time with boundary. It does not have to be a cylinder as in the usual Hamiltonian framework. Then we outline formal semiclassical quantization in the finite dimensional case. Towards the end we give an example of such a quantization in the case of abelian Chern-Simons theory.