This text is intended to be used for an upper-division course in geometry suitable for any mathematics major whether he intends to teach, to work in industry, or to do graduate work in mathematics. In order to be of use to all three of these groups such a course must help train high school teachers, prepare students for further study in mathematics, and develop the student's geometric intuition. It is the author's contention that a course in euclidean geometry centered around the theory of convex sets is admirably suited to meet these objectives.