Consider a polynomial ring T on n variables over a ground field k, and standard graded by the degree of each variable being 1. Let I be a graded ideal. The graded k-algebra Q=T/I is Koszul if k has a linear free resolution over Q, that is, the entries in the matrices of the differential in the resolution are linear forms (in this case, we also say that the ideal I is Koszul). Koszul algebras were formally defined by Priddy (who considered a more general situation which includes the non-commutative case as well). They appear in many areas of algebra, geometry, and topology. Two of their elegant properties are that the minimal free resolution of k can be explicitly described as the generalized Koszul complex, and there is a simple formula relating the Hilbert function of Q and the Poincare series of k (which is the generating function of the minimal free resolution of k over Q). Another important property of commutative Koszul algebras is that they are the algebras over which every graded finitely generated module has finite regularity. The talk will be a survey on Koszul Algebras.