Topics in several complex variables

Multidimensional Cauchy integral formula, uniqueness of analytic continuation, maximum modulus principle.
Hartog's theorem. Inhomogeneous Cauchy-Riemann equations. Holomorphic implicit and inverse function theorems.

De Rham bicomplex, Dolbeault complex, holomorphic de Rham complex of an open subset of $\mathbb{C}^n$. The Dolbeault complex is acyclic for polydiscs. Strict pluri-sub-harmonicity and pseudoconvexity.

Complex manifolds. $\mathbb{C}P^n$. Affine and projective non-singular algebraic varieties.

$X$ complex compact implies $\mathcal{O}(X)=\mathbb{C}$, so...

... presheaves, sheaves, cohomology of sheaves. Sheaf-theoretic proof of de Rham theorem.