Abstract: In this talk we take a look at a class of Hopf algebras that help us to combinequantum mechanics and gravity. We observe that the certain Hopf algebras naturally appear in the physics are self dual and noncommutative and noncocommutative. We are mainly interested in the representations of such Hopf algebras and their roles in physics. Many examples are provided to make a base for further discussions. The lectures are accessible by graduate students with or without algebra background.