The present text is an introduction to the theory of association schemes. We start with the definition of an association scheme (or a scheme as we shall say briefly), and in order to do so we—x a set and call it X. We write 1 to denote the set of all pairs (x,x) with x? X. For each subset X— r of the cartesian product X×X, we define r to be the set of all pairs (y,z) with (z,y)? r.For x an element of X and r a subset of X× X, we shall denote by xr the set of all elements y in X with (x,y)? r. Let us—x a partition S of X×X with?? / S and 1— S, and let us assume X— that s— S for each element s in S. The set S is called a scheme on X if, for any three elements p, q,and r in S, there exists a cardinal number a such pqr— that|yp?zq| = a for any two elements y in X and z in yr. pqr The notion of a scheme generalizes naturally the notion of a group, and we shall base all our considerations on this observation. Let us, therefore, briefly look at the relationship between groups and schemes.