Page "Seifert–van Kampen theorem" Paragraph 32

Fundamental groups also appear in algebraic geometry and are the main topic of Alexander Grothendieck's first Séminaire de géométrie algébrique ( SGA1 ).

A version of van Kampen's theorem appears there, and is proved along quite different lines than in algebraic topology, namely descent theory.

A similar proof works in algebraic topology, see.