The analogy between the crystal optics and the optics in photonic crystals is examined. By developing the group theory fur the anisotropy of crystal optics, it is shown that the analogy comes into play quite naturally and that photonic crystals embody the well-known characteristics of crystal optics in a much more striking way. Multi-birefringence effect, existence of singular points in equi-frequency surface of photonic bands and their effects on Light transmission are discussed, using some numerical results of a model photonic crystal.