The term "Quantum Group" is due to V. Drinfeld and it refers to special Hopf algebras, which are the non-trivial deformations ("quantizations") of the enveloping Hopf algebras of semisimple Lie algebras or of the algebras of regular functions on the corresponding algebraic groups. These objects first appeared in physics, namely in the theory of quantum integrable systems, in the 1980's, and were later formalized independently by Vladimir Drinfeld and Michio Jimbo. In this talk I will explain the main idea of deformation and introduce the simplest and historically the first example of a Quantum Group: $U_q(\mathfrak{sl}(2))$.