The purpose of this paper is to present the figure of Sophie Germain, setting her in the historical period in which she lived, and to try to explain some of the mathematical tools she used in her attempt to solve one of the most famous theorems in the history of mathematics: Fermat’s Last Theorem. Though the French mathematician gave some important results concerning Fermat’s problem, historically she has not been given credit for what she proved, until recent studies have re-evaluated her works. In the first and second section we present Sophie Germain’s biography and introduce Fermat’s Last Theorem from the algebraic point of view. The following sections are dedicated to the presentation of the most important results by Sophie Germain and the techniques she uses to prove them. Finally, we briefly discuss the failure of her plan, the so called “Grand Plan”, to prove Fermat’s conjecture.
