For questions about Hopf algebras and related concepts, such as quantum groups. The study of Hopf algebras spans many fields in mathematics including topology, algebraic geometry, algebraic number theory, Galois module theory, cohomology of groups, and formal groups and has wide-ranging connections to fields from theoretical physics to computer science.

**Hopf algebras**, named after Heinz Hopf, was first introduced in the theory of algebraic topology, while studying cohomology of Lie groups, but in recent years has been developed by many mathematicians and applied to other areas of mathematics such as algebraic groups, combinatorics, mathematical physics and Galois theory.

It is a structure that is simultaneously a (unital associative) algebra and a (counital coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism, called antipode, satisfying a certain property.

The representation theory of a Hopf algebra is particularly nice, since the existence of compatible comultiplication, counit, and antipode allows for the construction of tensor products of representations, trivial representations, and dual representations.

There is a wide variety of variations of the notion of Hopf algebra, relaxing properties or adding structure. Examples are weak Hopf algebras, quasi-Hopf algebras, (quasi-)triangular Hopf algebras, quantum groups, hopfish algebras etc.

For more details you may find the following references:

$1.~~$ "Introduction to Hopf algebras and representations" by Kalle Kytola

$2.~~$ "Hopf Algebras in Combinatories" by Darij Grinberg & Victor Reiner

$3.~~$ "Hopf Algebra" from Wikipedia

$4.~~$ "A Very Basic Introduction to Hopf Algebras" by J.M. Selig