Polarization provides a powerful degree of freedom for controlling light in optical systems. A light wave can be represented as two orthogonal components, and their relative amplitudes and phases define its polarization state. Fully polarized light is described by Jones vectors and matrices. Partially polarized or unpolarized states require the Mueller formalism. This chapter introduces the mathematical frameworks for describing polarization, including Jones and Mueller representations, and outlines practical approaches to generating and analyzing linear and circular polarization. Common polarization elements such as polarizers, retarders, and birefringent prisms are discussed, together with devices for broadband control, such as the Fresnel rhomb. Applications range from microscopy and laser optics to liquid-crystal displays, optical isolators, and astronomy.