A survey of modern algebra,

I have just started reading this book, and already I am enthralled by the beauty and elegance of the authors' exposition. Assuming nothing more than an acquaintance with school algebra and a little geometry, they develop the basic properties of central algebraic structures, including rings, groups and fields. These are treated by reference to familiar examples, such as the ring of integers and the rational, real and complex fields. Everything that one learned in school algebra is to be found here, though, as is to be expected, each topic is treated at a rigorous, mathematically sophisticated level. In the first two chapters, the properties of the integers and rational numbers are gradually examined, ultimately down to the definition of addition and multiplication on the basis of Peano postulates. The authors then consider polynomials, the real and complex numbers, vector spaces, linear algebra and other topics. The writing style is clear, concise and elegant, with each new concept being carefully defined as it is introduced. The proofs achieve a satisfying balance between detail and brevity. Indeed, reading the proofs and completing the exercises would do much, I am sure, to enhance a reader's mathematical facility.If you are interested in acquiring a deeper understanding of algebra, this book should serve as an excellent introduction.