We are deeply saddened by the passing of Martin Gardner on May 22, 2010. It is the end of an era in the world of popular and recreational mathematics. Thus this book is dedicated to his memory.

Martin's legacy in popular and recreational mathematics is legendary, though he modestly insisted that he was not a mathematician but a mathematics journalist. His background was in literature and philosophy, and his most famous book is The Annotated Alice. In honor of Martin, we invited the denizens of Lewis Carroll's Alice in Wonderland and its companion volume Through the Looking Glass to grace the pages of this volume and guide us through our mathematical adventures.

We strongly believe that the primary reason many students are having difficulty with mathematics is that they are bothered by the language of mathematics. By having Alice and the twins, Tweedledum and Tweedledee, serve as the protagonists in this volume, it is hoped that the students may find the conversational style less daunting to read than formal mathematics.

Alice and the twins are featured prominently in Chapter Zero, which is intended as assigned reading. They also introduce us to all subsequent chapters. As the students become more comfortable with the subject, the conversations recede to the background so as not to be overly distracting.

We have taken many excerpts from both books, but also bent them to our purpose. We hope Lewis Carroll would pardon the liberty we had taken, especially in mixing the characters between the two books. We wish to arouse sufficient interest in the students so that they would actually read and enjoy these two books, other works of Lewis Carroll, and classical literature in general.

At the University of Alberta, this book is used as a text for a contents course, offered by the Faculty of Science, for students in the elementary education program. These students also take Curriculum and Instruction courses from the Faculty of Education. Although the book has these students in mind all the time, it does not offer much pedagogical advice. We leave this to the experts.

Even as a text for a contents course, the book is still somewhat idiosyncratic and unorthodox. Many instructors may see it more as a classroom resource. Also, because its entry point is set at the ground level, the book is very suitable for self-study, life-long learning as well as liberal arts education.