Modernizing the teaching of advanced geometric optics

Advanced geometric optics has been traditionally presented to students as subjects of great mathematical complexity. In addition, there is confusion and misunderstanding about the nature of aberrations. We show here how to improve understanding and make the material more enjoyable through the use of the following pedagogic devices: (1) A matrix approach to paraxial optics. (2) A numerical treatment of non-paraxial optics and aberrations.