The topic of this master thesis are distance regular graphs. The thesis is divided into four sections and an appendix. After an introduction to graph theory we define distance regular graphs and their main properties. We give some essential examples of distance regular graphs, and we elaborate strongly regular graphs, which are the special case of diameter 2. In further development of the theory we introduce matrices and give the definition of the distance regular graphs through them. We give some main statements, proofs and results regarding the distance matrices of the distance regular graphs and their products. In the last section we introduce association schemes and their relation to distance regular graphs. We mention the Bose-Mesner algebra and all the parameters related to association schemes and how they are connected with intersection numbers of distance regular graphs. Lastly, we mention P-polynomial schemes and two most important examples. The appendix contains a table of small distance regular graphs and their intersection arrays.