The first volume, known as FGED1, begins with conventional treatments of topics such as linear algebra, transforms, and geometry. Then, it introduces Grassmann algebra and geometric algebra to provide a much deeper understanding of the subject matter and highlight the places where traditional arithmetic with vectors, matrices, quaternions, etc., isn't quite correct.
Below is the full table of contents. The book includes 49 figures, 15 tables, 36 code snippets, 62 exercises, and 327 numbered equations.