Abstract: The main objective of this talk is to describe the Lenstra elliptic-curve factorization algorithm. It's a fast integer factorization algorithm (third fastest known method, fastest for small primes) developed by Hendrik Lenstra in 1987. In order to understand it, we'll first go through some basics of elliptic curves, group theory, and Pollard's p-1 method (which Lenstra's method builds upon). No prior knowledge of elliptic curves is necessary for this talk to be accessible.