The Shape of Algebra in the Mirrors of Mathematics is a unique text aiming to explain some elements of modern mathematics and to show its flavor and unity. It is neither a standard textbook nor a tour of algebra for a casual reader. Rather, it is an attempt to share authors' mathematical experiences and philosophy with readers who have more than a passing interest in mathematics, but only a traditional exposure to High School Algebra and some elements of Calculus. The book gives the readers a sense of visual nature of significant part of mathematics. The reader becomes an owner of and a...