This chapter presents the results for deep learning theory from the perspective of hypothesis complexity, including the Vapnik-Chervonenkis (VC) dimension, the Rademacher complexity, and the covering number. By determining upper and lower bounds for the VC dimension of neural networks, we can better understand their generalizability. Additionally, we discuss margin bounds, which offer more robust generalization assurances compared to worst-case bounds based on the VC dimension. These bounds ensure that trained models can achieve a small empirical margin loss with high confidence. Furthermore, we examine the effect of residual connections on hypothesis complexity by analyzing the covering number of the hypothesis space. We propose an upper bound for the covering number, providing insights into how residual connections influence model complexity.