Algebra with Galois Theory (Courant Lecture Notes)

This book is fun. Everyone who is interested in abstract algebra should read it. Artin's style is very intuitive, the clear remarks and comments add to the streamlined demonstrations. The exposition has some original details usually abscent from more modern books on the subject. For example, Artin defines a ring as a set where addition is not necessarily assumed to be commutative; then he derives the result that if the distributive laws apply then addition IS necessarily commutative (i.e., a+b=b+a) for every element expressible as a product. Obviously, in a ring with units this is always true. Someone could validly ask "Why isn't there systems of double composition where both operations are non commutative"?, and Artin anwers that that "Seldom happens" (i.e., such a generalization is of small use, if any) .This books is not even similar to Artin's "Galois Theory"( Galois Theory: Lectures Delivered at the University of Notre Dame (Notre Dame Mathematical Lectures, Number 2) ), which is very succint and covers the contents in a different order. I recommend this one first, though both are valuable as a source. A good complement to this book (and by "complement" I do not mean that each one complements each other's contents, but rather having two different expositions on the same subject helps understanding)is John Stillwell's  Elements of Algebra .

Actually, I found this book not to be very useful.In my opinion it would probably be interesting toread for someone who already knows the subject quitewell. I've had van der Waerden and Birkhoff-MacLanefor many years, and I consider these to be far bettertext books.