The main objects studied in this thesis are association schemes. An association scheme with d classes is a set of spanning subgraphs G0,G1, . . . ,Gd which partition the edges of the complete graph Kn and have the property that for every two vertices x and y which are adjacent in Gk the number of vertices z adjacent to x in Gi and adjacent to y in Gj depends only on the indices i, j, k. This number is denoted by pk i,j and called an intersection number of the scheme. We can construct association schemes using distanceregular graphs and the most important examples are Johnson and Hamming schemes. Constructions using Ąnite groups are very important as well. AThe adjacency matrices of association scheme graphs span a commutative algebra called the Bose-Mesner algebra. The Bose-Mesner algebra of the association scheme is also spanned by idempotent matrices which are determined by eigenspaces of the adjacency matrices. Apart from the intersection numbers, there are other important parameters of the association scheme such as eigenvalues, dual eigenvalues and Krein parameters. These parameters have interesting dual properties. Association schemes obtained from distance-regular graphs are equivalent to P-polynomial schemes, and can also be characterized via intersection numbers, eigenvalues of the scheme and diameters of its graphs. There are also Q-polynomial schemes with characterizations via dual terms, but no combinatorial interpretation such as distance-regular graphs is known. Examples in the thesis were calculated using the GAP package AssociationSchemes.