This book will be an in-depth textbook introducing and covering all topics related to the fact that light is a transverse electromagnetic wave. It will begin with a discussion of the history of Maxwell's equations, from which the wave properties of light were first deduced, and then move into the fundamentals of electromagnetic waves, such as the polarization of light, energy and momentum conservation, and basic solutions of Maxwell's equations. From there, it will move into more practical topics: light propagation in matter of various types, light propagation through interfaces, light propagation in waveguides (like fibre optic cables), and light scattering.