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Basic Notions of Algebra (Encyclopaedia of Mathematical Sciences)

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The author explains not just the definitions but also the 'philosophy' of algebra with highly non- trivial examples from geometry,analysis & topology not to mention algebra itself. Examples motivate the concepts and show their usefulness. There is little number of formal proofs, but theorems are usually supported by natural 'explanations' which may be even more adequate. Frequently a single example in this book can replace a substantial theory of the corresponding subject. For example, about axioms of projective geometry. A reader with no knowledge of modern algebra can try reading it ,but it would be more interesting if familiar with subjects of undergraduate mathe matics. Then an undergraduate reader will get some ideas how modern math uses sophiscated tools from algebra to understand other subjects. Another merit of this book is that it can be smoothly followed by the author's famous 2-volume textbook on algebraic geometry.

An off-hand account of algebra by one of the best authorities of the subject. Recommended as a "serious" pass-time.