Abstract: This talk is an introduction to the main topic of my PhD thesis and it is based on the paper The Nodal Cubic is a Quantum Homogeneous Space by Ulrich Kreahmer and Angela Tabiri. I will give a brief introduction to the theory of Hopf algebras with examples, establish a correspondence between affine algebraic groups and commutative Hopf algebra and finally show that the nodal cubic is a quantum homogeneous space.