In ILWIS Projections are used by Coordinate systems to defines the relation between the map coordinates (X,Y) and the geographic coordinates latitude and longitude. The Earth's surface is curved, however in maps it is presented as a flat surface. Therefore, the display of an area on a map will always lead to some deformation or distortion; there is no 'perfect' projection. If you show only a small part of the Earth, like a town, the distortion will be almost insignificant. If, on the other hand, a map shows a continent, deformations and distortions will be a major problem. To correctly represent the curved Earth's surface on a flat map, you need a special projection. The geographic coordinates are converted to a metric coordinate system, measuring the X- and Y-directions in meters. Each projection has unique equations for the transformation from geographic to metric coordinates and vice versa.
Because of the earth's rotation, the shape of the earth is not a perfect sphere. The earth is flattened towards the poles: the equatorial axis (diameter of the equator circle) is longer than the polar axis. The shape of the earth can be represented by an ellipsoid, or as it is sometimes called, a spheroid (shapes that are generated by revolving an ellipsis around its minor axis). The choice of the ellipsoid which fits best a certain region of the earth surface to be mapped depends on the surface curvature and geoid undulations in that region. Hence every country has its own 'best fit' ellipsoid.