Supergeometry is fundamentally the study of Z2-graded spaces, which turns out to yield a rich counterpart to ordinary algebraic geometry. In this talk, we'll discuss the fundamental constructions of super-algebraic geometry. In particular, we will introduce the algebraic tools, including supercommutative superalgebras, their modules, and super Lie algebras, and then treat the details of superspaces, superschemes, and supergroups. We will also outline how the algebro-geometric picture of manifolds extends neatly to the supergeometric setting. Time permitting, we will conclude with some of the fundamental theorems concerning these structures, e.g., Deligne's tensor category theorem and Batchelor's theorem.