These notes aim to expand on the Complex Manifolds notes previously written. While those notes focues on Calabi-Yau manifolds from a differential geometry perspective, these notes we introduce the algebraic geometry techniques in order to study them. We show how to construct what are known as toric varieties from so-called fans. This approach is almost a trivial combinatorics game, and provides a very powerful and useful way to construct Calabi-Yau manifolds with desired properties. To read more either click the image above or here.