Abstract: 

We all know Galois the algebraist — the creator of group theory and Galois theory, the tragic genius who wrote his testamentary letter the night before the fatal duel. I want to introduce you to a different Galois: Galois, the analyst. And I want to show you that in his letter, he wrote down amazing results and vast programs in analysis: abelian integrals, their periods, the global topology of algebraic curves, transformations of abelian integrals, which would take mathematics decades to fully realize.