Hopf algebras were discovered in 1941 by Heinz Hopf in algebraic topology, but a general theory of these algebras began in the late 1960s. 

In 1975 Kaplansky listed 10 conjectures on Hopf algebras, which have been the focus of a great deal of research. Some of these conjectures are still open. The one we are interested in is the sixth one, which is about representation theory for Hopf algebras. 

The aim of this talk is to present the research work around this conjecture. In order to reach this goal, we will firstly recall what a Hopf algebra is. We will focus on some examples, especially on group algebras. Moreover, we will explain Drinfeld twist, that is a way to deform Hopf algebras, by means of an invertible element.