The book is devoted to various problems arising in electromagnetic field interacting with matter. It belongs to what is usually called Electrodynamics of Continuous Media, or Classical Electromagnetism in Matter, or Optics and the Theory of Electrons. These subjects are usually left at a quasi-empirical or semi-phenomenological level. The present book introduces explicitly the degrees of motion of the electric polarization and magnetization of matter. This new approach renders Maxwell equations in matter a determined system of equations and allows specific solutions for a series of problems which might be of interest in today's nanoplasmonics and nanophotonics. The book includes both a basic exposition of fundamental things in Electromagnetism and various particular problems, some of them collected from papers published in scientific journals.