Koszul Algebras and Linear Modules: An introduction to the theory of Koszul algebras and linear modules.
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In this thesis Koszul algebras and their modules, so called linear modules, are introduced. In order to do so, graded $K$-algebras, where $K$ is a field, are also defined and discussed. Furthermore, an isomorphism between split basic finitely $1$-generated graded modules and a path algebra $KGamma/I$ is proved. Linear resolutions are discussed as a preliminary for Koszul algebras. Lastly, the Yoneda algebra $E(Lambda)$ is studied more closely in the case when $Lambda$ is Koszul.