What is a system for mapping around earth on a flat surface called

There are a few systems. For most maps you find either Universal Transverse Mercator projection [U.T.M. for short] or Lambert Conformal Conic. These two projections are most common for mapping regions of the Earth's surface to maps, and for determining coordinates for GPS.Source:Geodesy is the science of positioning places on the Earth's surface. Cartography is the science of using rules from Geodesy to make maps.