Pell's equation is part of a central area of algebraic number theory that treats quadratic forms and the structure of the rings of integers in algebraic number fields. It is an ideal topic to lead college students and talented high school students to a better appreciation of the power of mathematical technique. To appreciate this focused exercise book, a high school background in mathematics is all that is needed, and teachers and others interested in mathematics who do not have a background in advanced mathematics may find that it is a suitable vehicle for keeping up an independent interest in the subject.