A-infinity algebras are algebras with a differential, a product, and a series of higher products which generalize matrix Massey products in topology. These objects come equipped with an appropriate notion of an A-infinity morphism. We plan to give an overview of notes by Bernard Keller, focusing on two important properties: A-infinity quasi-isomorphism between any dg algebra and its cohomology (with some non-trivial A-infinity structure) and interpreting various categories as modules over an A-infinity algebra.