This course covers foundation and recent advances of deep neural networks (DNNs) from the point of view of statistical theory. Understanding the power of DNNs theoretically is arguably one of the greatest problems in machine learning. During the last decades DNNs have made rapid process in various machine learning tasks like image and speech recognition and game intelligence. Unfortunately, little is yet known about why this method is so successful in practical applications. Recently, there are different research topics to also prove the power of DNNs from a theoretical point of view. From an aspect of statistical theory, several results could already show good convergence results for DNNs in learning different function classes. The course is roughly divided into two parts. In the first part, DNNs are introduced and different network architectures are discussed. In the second part, we focus on the statistical theory of DNNs. Here we will introduce frameworks addressing two key puzzles of DNNs: approximation theory, where we gain insights in the approximation properties of DNNs in terms of network depth and width for various function classes and generalization, where we analyze the rate of convergence for both, regression and classification problems.