Complex light refers broadly to beams of light where one or more parameters are changed within the beam of light. In this chapter, the author delves into complex light by treating the most important beams of light that are useful for research in many areas of science and technology. He includes a description of the functional forms of the modes and their parameters, which lead to better resolution and deeper penetration. The author discusses optical beams that are described by a Gaussian intensity profile. This is the case of laser beams. Thus it is important to begin with a discussion of the fundamental Gaussian beam and its properties. The authors derives the equation of the fundamental Gaussian beam. This treatment is also covered in standard textbooks on lasers. In classical electromagnetism, light is represented by an electromagnetic wave, with electric and magnetic fields that obey Maxwell’s equations.