This is a textbook about plane geometry. It will be divided into two volumes, Geometry without Multiplication: White through Red Belt and Geometry with Multiplication: Blue through Black Belt. The white- and yellow-belt chapters are absolute geometry; the remainder of Volume One and all of Volume Two is Euclidean geometry. It is primarily intended to train mathletes for competition, but it also provides geometry needed by engineers and military officers; the discussion of machine gun emplacement is of interest to most boys, even if they do not plan to enlist. The early chapters prepare students for jobs in construction, architecture, surveying and graphic arts.