This thesis presents the path integral formulation of quantum mechanics, focusing on deriving the propagator from the Schrödinger equation. The general propagator is then derived using the transition amplitude for short time intervals and the path integral approach. Then, the propagators of the free particle and the harmonic oscillator are determined. Finally, the path integral formulation is used to study the Aharonov-Bohm effect. The thesis finishes with some discussions about the classical limit.