We define geometry, in its broadest sense, as the mathematics of shape, dimension, symmetry and position. Our aim is to cover each of these facets, in varying depths. Our deepest coverage relates to the various topics introduced in The Shape of Things. We also reexamine the Real numbers introduced in A Number Tree and extend this 1-dimensional system to a 2-dimensional case; the Cartesian Plane. Next, we briefly acquaint the reader with the important topic of symmetry.
At this point we introduce the subject of metric spaces. This provides a helpful bridge between the first three topics and the often more abstract field of topology, the mathematics of position.