Modular forms arise in the study of various questions of elliptic curves, number theory, and even string theory. They are complex functions that obey beautiful symmetry patterns. Primary examples of modular forms are the Eisenstein series. This talk will present some foundational results on modular forms on the full modular group, including a description of a result by Rankin and Swinnerton-Dyer restricting the locations of the zeros of the Eisenstein series.