Due to the nature that the class number is closely related to how far the unique factorization will fail for a ring, it is important to calculate the class number. Historically, it was Dirichlet who fully proved the special case of the quadratic field using analytical method in 1839. In this talk, we will discuss what the class number formula is, sketching of the proof, and, if time allows, the connection to the quadratic forms. Speaker(s): Yiwang Chen (UM)