Answer
Sheaf Theory is not a mathematical area that Grothendieck advanced. Instead, he made significant contributions to other areas such as algebraic geometry, category theory, and homological algebra. Sheaf Theory was introduced by Jean Leray in his study of topology and differential geometry. Grothendieck applied sheaf theory extensively in his work, but he is recognized for his breakthroughs in the above-mentioned areas, which had a profound impact on modern mathematics.