By "elementary algebra" we mean the material found in American high school and college algebra courses. This material consists of a selection of topics drawn from the broad area of mathematics known as algebra. The material presented in a traditional elementary algebra course is only a small part of the whole body of algebra. Indeed, a traditional course consists of material that was all developed before the mid nineteenth century, while the greater part of algebra was developed in the twentieth century.

The obvious way to study any subject is to "start at the beginning and continue until you reach the end". The problem with that approach is that it assumes that there is a clear cut choice for "the beginning" and an unambiguous path to follow to "the end". Many subjects do not satisfy those assumptions -- the material, rather than than forming a straight line, may have a more complex form such as that of a forest where there is more than one point of entry, few clear cut paths and trees everywhere blocking ones view of the forest as-a-whole. I believe that algebra is such a subject. At most points in the subject there is more than one choice of where to go next. Perhaps the material a some point seems obvious to some students yet totally obscure to others. The first group will want to go to a new subject, the other group will want to look at the current subject, but from a different viewpoint. Some students will be content with learning just the bare bones of a given subject, others will want to "look inside the box" to see how and why everything works. The eventual goal in writing (and rewriting) this book is to make it possible to take many different paths through (and even beyond) the algebraic forest. The device that makes it possible to take many different paths is the use of hypertext. The device that makes it possible to continuously rewrite and extend the book is that fact that it is on-line rather than in-print.

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