In this book, Isaac Asimov has reduced the complexities of a branch of mathematics to terms that anyone can understand. In an easy and informal style, he proceeds painlessly from the most basic concepts of algebra to the more refined considerations of quadratic and cubic equations, simultaneous equations, and those involving imaginary and transcendental numbers.

Also included are illustrations of the way algebra can be used in everyday life, as well as the role it played in the discoveries of Galileo and Newton. “The real importance of algebra, and of mathematics in general,” writes Professor Asimov, “is not that it has enabled man to solve this problem or that, but that it has given man a new outlook on the universe. From the time of Galileo onward, mathematics has encouraged man to look at the universe with the continual question: ‘Exactly how much?’”

This is the third of the “Realm” books and probably the slightest. It lacks the overpowering breadth of Realm of Numbers and (to some extent) the sheer practicality of Realm of Measure. Now, before I be taken to task for being a mathematician who denies the practicality of algebra, let me say in my own defense that you really don’t learn an awful lot of algebra here. As with the other two books, it starts off extremely slowly—you‘re nearly halfway through before you do any involution or evolution, and problems such as linear and quadratic equations are left to the very end.

The book also suffers from a rather distracting typesetting—there are a lot of fractions, which tends to make the line spacing uneven.

Finally, Realm of Algebra relies rather heavily on the other two books and refers to them frequently. This is something Asimov does a lot, and one is never sure whether it is a marketing ploy or a way to avoid having to “stop and explain”—probably, in this case, the latter. Still, the trilogy might have been better conceived originally as a set of three which someone reads in order (rather like The World of Carbon and The World of Nitrogen), rather than three separate but closely related works.

That aside, it is not a bad book by any means. As with many an Asimov volume, it suffers not so much from an inherent lack of value as simply by comparison to the volumes around it.