Abstract A polymer is a large molecule made up of many small, simple chemical units, joined together by chemical reaction. For example, polyethylene As with most other substances, in order to understand the properties of polymeric materials we must consider a large assembly of molecules. However, in the case of polymers, the molecules themselves are very large, and we need to use statistical mechanics to calculate the characteristics of even an isolated polymer. One way to investigate the properties of a single polymer is to place it in a very dilute solution, so that interactions between the polymers can be neglected. Experimentally, such dilute polymer solutions are used to determine the size and molecular weight of the molecule. In this chapter, we will theoretically investigate the properties of an isolated, single polymer chain in solution.