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Quantum groups were unleashed to the world by Drinfeld in his 1986-ICM address. They are represented by Hopf algebras. Initially developed by Drinfeld with applications to physics in mind, quantum groups interacted with a number of other interesting objects. In this talk, we shall try to convey some of the original motivations for introducing quantum groups. No background will be assumed. We shall start from the very basic, by introducing what a Hopf algebra is, and go as far as providing systematic solutions of the quantum Yang-Baxter equation. Time permitting, we shall try to look at them from an analytic perspective and introduce what are called Compact quantum groups a la Woronowicz. |