The interacting particle system is a dynamic system that contains a lot of interacting particles. Because of the interaction between different particles, the direct analysis and simulation of the system are very difficult. The mean-field analysis is a framework for analyzing these large interacting particle systems. In this framework, instead of directly studying the coupled system, one approximates the system by a partial differential equation whose solution characterizes the distribution of the particles. This strategy largely simplifies the problem and provides a more efficient way to study the evolution of the particle system. In this talk, I will mainly focus on the derivation of the mean-field analysis and its application in analyzing overparameterization of neural network.