A map projection is a systematic transformation of the latitudes and longitudes of locations on the surface of a sphere or an ellipsoid into locations on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. There is no limit to the number of possible map projections.
Please review the following articles in detail:
Please go through this Lecture of your course
Chpater 1 maps from this site http://planet.uwc.ac.za/nisl/GIS/Power_Point/ (need to download and go through the Power Point)
You can explore Projections using this resource: http://planet.uwc.ac.za/nisl/GIS/Projections/ (you need to have Java installed for the application to work).