The document discusses the seven crystal systems and their defining characteristics. There are three main crystal systems - cubic, tetragonal, and orthorhombic. The cubic system has three equal cell vectors of length a that meet at 90 degree angles. The tetragonal system has two equal cell vectors of length a that meet at 90 degrees, while the third vector c is unequal in length and also meets at 90 degrees. The orthorhombic system has three unequal cell vectors a, b, c that all meet at 90 degree angles.