Abstract: In this talk, we will introduce martingales and stopped martingales. Using the stopped martingale, we will analyze some of the properties of the simple symmetric random walks. In particular, we will discuss the first collision times of two or three random walks and compute some of the basic distributional property (such as expectation) of the collision time. A part of the talk is based on joint work with D. Coupier, K. Saha and Chi Tran.