Algebra

It's really an amazing book. The quality of pages, the printing and overall of whole book is good. I definitely suggest to buy this book if you want to invest your time, money & energy in some good book.

I saw some reviews which ridiculed this book because it wasn't transparent and had incomplete proofs. So, I feel obliged to make it clear what the vision of Author is and whom this book is for. First it's a Graduate text so it assumes undergraduate knowledge and summarizes them to get to the real content early. It's Aim is to be Concise and Comprehensive which is a gem for someone who's already mathematically initiated and only needs little guidance to proceed. This Style may look confusing to uninitiated ones and I recommend they checkout books like J. A. Gallian, I.N. Herstein and Dummit and Foote. Dummit and Foote is another gem. For those who knows how to read this book it's the most Clear, Elegant and Complete Book for Algebra. Serg Lang is Renowned both as a Mathematician and as an Author. One quality of his is he writes a book as he learns or revises those concepts, giving it a natural style and raw Exposition. I've partially read all of his books and it's a tremendously pleasurable experience.

It is not often that an author of a graduate textbook shares their understanding rather than merely provide a collection of theorems and proofs. Lang always delivers on this front. I'm partial to analysis myself, so I was certainly hesitant picking up this tome. But you'll find that it has everything you need (and much more). I primarily used the first four chapters, as well as the chapter on algebraic varieties. Each chapter is concise and written in a conversational style. There are many many great exercises as well.

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I love this book. It is, of course, not meant as a first exposure, but it is an amazing read if you are familiar with the basics of algebra. Every time I see some algebraic construction that I'm not familiar with I just look it up in Lang and read some epsilon-neighbourhood of the construction. The point is, the text is SO WELL ORGANISED that you really can learn about constructions and theorems and even general theories etc. very very quickly if you know what it's supposed to be about (i.e. if you don't need 5 pages of motivation and various visualisations etc.). The constructions and arguments leading to theorems and so on are almost always clearly recognisable. Also, great, huge list of references about anything of interest that comes up in the text (more specific references being at the end of the corresponding bits). Even if you don't buy it now, a time WILL COME that you'll want to have this book on your shelf.

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