In this lecture I will focus on the application of Mathematica to study polarization of light beams, formation of optical lattices, properties of structured light (light with angular momentum).  We will present Mathematica as a tool to discuss and to solve examples from optics. The intention of this lecture is to demonstrate the usefulness of Mathematica in wide range of applications. We will not give a complete description of its syntax but demonstrate by examples the use of its language. In particular, we show how this modern tool is used to solve classical problems like propagation of electromagnetic waves, including boundary conditions on the interface between different materials (different refractive index). Next we will solve nonlinear propagation equations and discuss special solution, like solitons, solitary waves, vortices etc. The main goal is to convince students that Mathematica can be used as convenient tool for fast estimates and “back of the envelope” predictions.