Quantum Field Theory and Functional Integrals

These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view, where the main focus lies in Euclidean field theory. The notion of Gaussian measure and the construction of the Wiener measure are covered. Moreover, we recall the notion of classical mechanics and the Schr\"odinger picture of quantum mechanics, where it shows the equivalence to the path integral formalism, by deriving the quantum mechanical propagator out of it. Additionally, we give an introduction to elements of constructive quantum field theory.