The concept of Hopf algebras was first introduced in the theory of algebraic topology but in recent years has been developed by many mathematicians and applied to other areas of mathematics such as Lie groups, algebraic groups and Galois theory. This book is an introduction to the basic theory of Hopf algebras for the reader already familiar with the basic ideas of linear algebra and commutative algebra. After introducing and discussing the basic properties of coalgebras, bialgebras and Hopf algebras, the author treats the fundamental structure theorem of bi-modules and Sullivan's proof of the existence and uniqueness of integrals of Hopf algebras. This book will interest graduate students and research workers who specialise in algebra.