Inspired by obvious symmetry and beauty of frieze patterns found on ancient buildings, fabrics, jewelry, pots etc., in this thesis we will look for possible ways for classification of those patterns from mathematical point of view. Mathematically speaking, friezes are geometrical planar patterns structured in such a way that they repeat themselves in one direction indefinitely. Depending on isometries combined we get various samples and based on that we discern frieze groups. The symmetry group of a frieze pattern is called a frieze group, and a proof that there are exactly seven types of frieze groups will be presented in the thesis. This classification is based on fact that the only possible motions for the frieze pattern are: translation along a fixed horizontal line L, 180 rotation about point on L, a horizontal mirror through L, vertical mirrors and glide symmetry. Examples will be provided for each of the seven groups. Further on, it will be shown how to recognize a type of group when one is presented with a pattern on an object such as a vase or a traditional Croatian dress. The final chapter considers the possibilities of various friezeusing activities in modern math class.