Sheaves of differentials.
Background on homological algebra : resolutions, derived functors, $\delta$-categories.
Triangulated categories, Derived categories of abelian categories.
Injective and flasque resolutions.
Cohomology of sheaves of abelian groups
Vanishing theorems for cohomology
Serreās criterion for affineness
\v{C}ech cohomology
Cohomology of projective space, twisting by Serre sheaves
$Ext$ and $Tor$ for sheaves
Serre duality theorem
Schemes as functors of points, the idea of stacks