Algebraic Space
Algebraic spaces extend schemes by allowing scheme charts in the étale topology. Use the representable diagonal and the surjective étale chart in the definition as a checklist, then check how schemes fit into the resulting category.
Before opening the references
Scheme · Sheaf · Representable Functor · Categorical Pullback
Where to read
Start here: The Stacks Project — Algebraic spaces
The Stacks Project Authors · Online reference · English · Free full text
Section 65.6, Definition 65.6.1, Lemma 65.6.2, and Definition 65.6.3
Continue from here
Algebraic Geometry in the library · Preparation and skip guidance