This chapter presents the hypothesis complexity concept frequently used in statistical learning theory, which is important for deriving generalization bounds for deep learning models. The hypothesis complexity characterizes the complexity of a machine learning algorithm and can be measured in terms of the Vapnik-Chervonenkis (VC) dimension, Rademacher complexity, and covering number. Intuitively, a more complex algorithm has worse generalizability. In this way, we may study the generalizability via the hypothesis complexity.