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Note publique d'information : This text aims to provide graduate students with a self-contained introduction to
topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras,
and Hopf algebras. The last chapter (Chapter 4) discusses several applications of
Hopf algebras, some of which are further developed in the author’s 2011 publication,
An Introduction to Hopf Algebras. The book may be used as the main text or as a supplementary
text for a graduate algebra course. Prerequisites for this text include standard
material on groups, rings, modules, algebraic extension fields, finite fields, and
linearly recursive sequences. The book consists of four chapters. Chapter 1 introduces
algebras and coalgebras over a field K; Chapter 2 treats bialgebras; Chapter 3 discusses
Hopf algebras and Chapter 4 consists of three applications of Hopf algebras. Each
chapter begins with a short overview and ends with a collection of exercises which
are designed to review and reinforce the material. Exercises range from straightforward
applications of the theory to problems that are devised to challenge the reader. Questions
for further study are provided after selected exercises. Most proofs are given in
detail, though a few proofs are omitted since they are beyond the scope of this book
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