Described here is Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view. Therein lies the main focus of Euclidean field theory. The notion of Gaussian measure and the construction of the Wiener measure are covered. As well, the notion of classical mechanics and the Schrödinger picture of quantum mechanics are recalled. There, the equivalence to the path integral formalism is shown by deriving the quantum mechanical propagator from it. Additionally, an introduction to elements of constructive quantum field theory is provided for readers.