Five shades of graded rings

Abstract: 

In ring theory, in many instances there is a possibility of partitioning the structure of the ring and then rearranging the partitions. These rings are called graded rings. This adds an extra layer of structure (and complexity) to the theory. We will discuss the natural grading of Leavitt path algebras, (these are algebras coming from directed graphs) and consider the category of graded modules. We study the information comes out of this grading. We recall the concept of the graded Grothendieck group and summarise the results on the classification of Leavitt path algebras via graded K-theory.