Abstract: A Skolem sequence of order t is a sequence of 2t integers such that each integer in the set {1, 2, ..., t} appears twice and the positions in the sequence equal to k, for each k in the set {1, 2, ..., t}, are k apart. For example S: 1, 1, 3, 4, 2, 3, 2, 4 is a Skolem sequence of order 4. Notice that the two 1's are right next to each other, the two 2's have one number in between them, the two 3's have two number in between them, etc. In this talk, we will discuss the many fascinating applications of Skolem sequences and how they are used to find cycle systems of complete graphs.