This talk is intended as a very basic introduction into Quantum Field Theory intended for mathematicians with background in PDEs or microlocal analysis.

I will explain the basic features of Quantum Field theory, Gaussian and quasifree states, Einstein causality and locality, and microlocal properties of propagators. 

If there is time I will sketch the perturbative construction of n-point functions based on causal perturbation theory and how regularisation and renormalisation appear naturally when working with distributions.