This modern textbook is based on the lectures and exercises of the authors on the theory of electromagnetic fields (electromagnetism) and advanced mathematics. As engineering increasingly demands more comprehensive and deeper mathematical and theoretical knowledge, the authors go beyond the usual curriculum of basic courses and particularly emphasize the topics of variational calculus and tensor calculus. They take an unconventional approach for engineers by deriving Maxwell's equations from the principle of least action using the aforementioned calculations. By introducing the principle of relativity and the principle of the constancy of the speed of light, the reader is given a straightforward entry into relativistic considerations.