Summary: Gravitational lensing provides a powerful tool to study a number of fundamental questions in astrophysics. Fortuitously, one can begin to explore some nontrivial issues associated with this phenomenon without a lot of very sophisticated mathematics, making an elementary treatment of this topic tractable even to senior undergraduates. We give a relatively self-contained outline of the basic concepts and mathematics behind gravitational lensing as a recent and exciting topic for courses in mathematical modeling or scientific computing. To this end, we have designed and made available some interactive software to aid in the simulation and inversion of gravitational lenses in a classroom setting.