Abstract: This introductory chapter discusses periodic and quasiperiodic crystals. Perfect quasiperiodic crystals and periodic crystals have sharp Bragg peaks, on the positions of a Fourier module. When the rank of the quasiperiodic structure is equal to the dimension of the space, the Fourier module is identical to the reciprocal lattice. A quasiperiodic crystal with a rank higher than the dimension of the physical space is called an aperiodic crystal.

Keywords: periodic crystals, quasiperiodic crystals, symmetry, lattice, aperiodic crystal,