Wu, Gang2016-09-212016-09-212016http://hdl.handle.net/10393/35197http://dx.doi.org/10.20381/ruor-155In this thesis, we present a detailed exposition of Koszul algebras and Koszul duality. We begin with an overview of the required concepts of graded algebras and homological algebra. We then give a precise treatment of Koszul and quadratic algebras, together with their dualities. We fill in some arguments that are omitted in the literature and work out a number of examples in full detail to illustrate the abstract concepts.enKoszul algebrasQuadratic algebrasKoszul duality.Thesis