This book is based upon a series of lecture notes written by the author for his courses in mathematical physics at Qiuzhen College of Tsinghua University. The essence of this book is to explain both the physical and the geometric aspects of modern electromagnetism, as well as the bridge between these two viewpoints. The first part of this book explains key ingredients of electromagnetic fields and their classical dynamics. The second part explains Maxwell theory in terms of the geometry of $U(1)$ fiber bundle. We use the language of differential forms throughout this book to illustrate the geometric and topological natures of Maxwell's equations.