Characteristic function is a very important tool in probability. It is directly connected to the Fourier transform, a fundamental object in many areas of science. It uniquely identifies a probability distribution, and is especially useful for handling sums of independent rvs. We shall show its connection to weak convergence and use it to prove the central limit theorem. For more information on characteristic functions, refer to Lukacs [1970], Lukacs and Laha [1964], and Ramachandran [1967].