Writing for freshmen and sophomores in college or advanced high school students, Lin (National Taiwan Normal U.) takes the view that recently geometric linear algebra has become too algebraic and tackles the subject from another angle, starting with the affine and linear structures of real vector spaces R1, R2 and R3, stepping through them as one-dimensional (including affine variants), two-dimensional (including linear transformations and affine transformations) and three dimensions, including lines and planes in space. In appendices Lin gives the background information necessary to follow the text and do the exercises, including an extended description of algebraic linear algebra. Annotation ©2005 Book News, Inc., Portland, OR (booknews.com)