Maxwell’s equations admit a rich array of wave-like solutions beyond the well-known plane waves and fundamental gaussian beam solutions. These solutions are distinguished by their phase and polarization profiles. Because their phase and polarization structures is integral to their definition, these solutions are referred to as structured beams. Among these structured beams, the so-called singular beams, which contain phase or polarization singularities, are especially interesting both from fundamental and applications standpoints. These lectures introduce the basic concepts used to describe these beams and show, starting with Maxwell’s equations, how different families of structured beam solutions arise. We will focus on Hermite-Gauss, Laguerre-Gauss, and Bessel-Gauss family of beams and their phase and polarization structure including phase and polarization singularities. We will also consider some techniques to realize these beams.