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.
