In this course we shall study the basic topic in additive number theory, the theory of partitions.  This topic begins with the fundamental question:  "How many ways can you write a given integer as sums of positive integers?"  In trying to answer this question we will be led to a variety of intriguing discoveries including some of those found by India's great, enigmatic genius, Srinivasa Ramanujan.  We shall also introduce the Omega Package (implemented in mathematica) in order to use the power of modern computer algebra to investigate partitions.