In this thesis, we explore the formalism of Feynman’s path integrals as an alternative approach to quantum mechanics (QM). The path integral connects classical and quantum theory through the principle of least action. In the introductory section, we illustrate fundamental quantum principles such as superposition using the double-slit experiment, and introduce the concept of quantum transitions as a sum over all possible paths. Furthermore, we demonstrate how the path integral formalism can be derived from canonical QM. We delve into techniques for computing path integrals, analyzing Gaussian integrals that aid in the calculation of propagators. We then focus on specific applications of path integrals to physical systems such as the harmonic oscillator, providing detailed calculations for propagators of more general Lagrangians. Finally, we investigate the connection between path integrals and statistical physics, explaining how partition functions can be computed using this formalism.