This is an advanced but very readable introduction to high school algebra for honors students, including as many Cartesian topics as can be presented without use of Euclidean geometry. These will include standard treatments of sets, numbers, equations in one variable, factoring, and functions, as well as more specialized topics such as linear programming that are considered interesting to the student. It is meant to offer an "understandable and accessible" honors course to students in the subject. It assumes a knowledge of multiplication by negatives, simplification of radicals, and other operations with numbers. The style of the text imitates that of most college level Analysis, or Advanced Calculus, texts, both for the sophistication it imparts and to best organize a difficult subject. Very interested students are almost assured to get through this excellent and well written course with only the slightest help from an ordinary tutor or committed instructor.