This half-day course will survey basic principles and developments in the field of photonic crystals, nano-structured optical materials that achieve new levels of control over optical phenomena. This leverage over photons is primarily achieved by the photonic band gap: a range of wavelengths in which light cannot propagate within a suitably designed crystal, forming a sort of optical insulator. The course will begin with an introduction to the fundamentals of wave propagation in periodic systems, Bloch's theorem and band diagrams, and from there moves on to the origin of the photonic band gap and its realization in practical structures. After that we will cover a number of topics and applications important for understanding the field and its future. Topics will include: the introduction of intentional defects to create waveguides, cavities, and ideal integrated optical devices in a crystal; exploitation of exotic dispersions for negative-refraction, super-prisms, and super-lensing; the combination of photonic band gaps and conventional index guiding to form easily fabricated hybrid systems (photonic-crystal slabs); the origin and control of losses in hybrid systems; photonic band gap and microstructured optical fibers; and computational approaches to understanding these systems (from brute-force simulation to semi-analytical techniques).