This book deals with electromagnetism, a fundamental subject for physics graduate students. Electromagnetism is a subject treated in the major technological schools, especially those related to telecommunications in the civil and military fields. In this book we deal with the basics of electromagnetism, in particular, the demonstration of Maxwell's equations and their applications. This cannot be done without knowing the basic formalisms including vector analysis, electrostatics and magnetostatics. The variation of the two electric and magnetic fields as a function of time is the first step in the study of electromagnetism. Thus, when we vary the electric field vector as a function of time, we create a magnetic field vector and vice versa. The two vectors vibrating as a function of time propagate in space and create what is commonly referred to as electromagnetic waves. We define, in this manuscript, the Poynting vector, the electric and magnetic energy densities, the electromagnetic power characterizing an electromagnetic wave.