This course deals with the engineering aspects of optics and its main emphasis is on applying the knowledge of optics to the solution of many engineering problems. The course is a graduate level class that covers the mathematical theory, the fundamental physical concepts and Matlab-based numerical implementations of Fourier optics for the design of diffractive elements, imaging systems and light propagation in complex media. The course will provide in-depth discussions of ray propagation in non-homogeneous and transformation media, Lagrangian and Hamiltonian optical design of inhomogeneous components (e.g. graded-index optics), scalar wave diffraction theory and inversion with emphasis on engineering applications to focusing, realistic imaging systems with aberrations, spatial light modulators, optical sensors, optical speckle patterns, and light propagation through random media. Generalizations to vector waves will also be provided when appropriate. The goal of the course is to present a consistent formulation of wave propagation and diffraction in complex linear systems for the engineering of advanced optical devices in strong partnership with computer simulations and engineering-led implementations. Numerous programming examples and notes will be provided per course topic and all students will be able to challenge their creativity in designing advanced optical devices as part of their course assignments and for the required final project.