The purpose of this book is to provide a concise yet detailed account of
fundamental concepts in modern algebra. The target audience for this
book is first-year graduate students in mathematics, though the first
two chapters are probably accessible to well-prepared undergraduates.
The book covers a broad range of topics in modern algebra and includes
chapters on groups, rings, modules, algebraic extension fields, and
finite fields. Each chapter begins with an overview which provides a
road map for the reader showing what material will be covered. At the
end of each chapter we collect exercises which review and reinforce the
material in the corresponding sections. These exercises range from
straightforward applications of the material to problems designed to
challenge the reader. We also include a list of 'Questions for Further
Study' which pose problems suitable for master's degree research
projects.