As long as there have been maps, cartographers have grappled with the impossibility of portraying the earth in two dimensions. To solve this problem mapmakers have created hundreds of map projections, mathematical methods for drawing the round earth on a flat surface. Yet of the hundreds of existing projections, and the infinite number that are theoretically possible, none is perfectly accurate. This study is a detailed history of map projections from before 500BC to the present. It contains a comprehensive collection of diagrams of the projections used in world mapping, with a compendium of information on their origins and use.