The path integral formulation is a method in quantum mechanics that describes the behavior of particles by considering all possible paths they can take between two points. Instead of focusing on a single trajectory, it sums over every conceivable path, assigning a probability amplitude to each one. This approach helps to calculate the likelihood of different outcomes in quantum systems. Developed by Richard Feynman, the path integral formulation provides a powerful framework for understanding quantum field theory and has applications in various areas of physics, including quantum electrodynamics and statistical mechanics. It emphasizes the role of probabilities and the wave-like nature of particles in quantum systems.