Many people seem to think that mathematics is a stagnant and finite field, consisting of algebra and geometry (the lesser of mathematical evils) and the other dreaded and unspeakable ones: mainly trigonometry and calculus. While these are undoubtedly the dominant topics covered in high school, anyone who has studied mathematics beyond the required level learns that mathematics is, in fact, an infinite and expanding field (pun intended). To illustrate this point, this article will explore the relatively recent and burgeoning topic within the topic of Ramsey Theory, providing a basic mathematical introduction to the topic. Ramsey Theory is a branch of combinatorics, which is the field of mathematics involving the study of sharp, discrete objects. In a general sense, Ramsey theory deals with the conservation of some properties of graphs under various circumstances. In more specific terms, Ramsey Theory asks how many vertices a graph must have to contain a complete s-subgraph or for the complement of the graph to have a complete t-subgraph, where sets are integers. This can also be explained in terms of edge c...