Grothendieck's 'Séminaire de Géométrie Algébrique'

Grothendieck's *Séminaire de Géométrie Algébrique* is a foundational collection of advanced mathematical lectures that revolutionized algebraic geometry. It introduces new frameworks for understanding geometric structures defined by polynomial equations, emphasizing abstraction and generality. By developing concepts like schemes, sheaves, and cohomology, Grothendieck provided powerful tools to study geometry in a broad, flexible way. While highly technical, the seminar fundamentally extended algebraic geometry's reach, influencing modern mathematics by bridging algebraic concepts with geometric intuition at an abstract level.