  This book provides an introduction to the mathematical analysis of deep
learning. It covers fundamental results in approximation theory, optimization
theory, and statistical learning theory, which are the three main pillars of
deep neural network theory. Serving as a guide for students and researchers in
mathematics and related fields, the book aims to equip readers with
foundational knowledge on the topic. It prioritizes simplicity over generality,
and presents rigorous yet accessible results to help build an understanding of
the essential mathematical concepts underpinning deep learning.
