On the presentation of Maxwell´s theory

Maxwell´s original work on electromagnetic theory is reviewed. All the general equations prominently displayed by the scientist in his two important works have been cast in modern notation with particular emphasis on the connotation. The relationship between two integral forms of the Faraday-Maxwell and the Ampère-Maxwell laws has been examined in detail, all within the framework of Maxwell´s theory, and using the conventional concepts of space and time. An example is given to show the exact nature of the integral form of the Faraday-Maxwell equation based on the Special Theory of Relativity. Some typical ambiguities found in many presentations of Maxwell´s theory are pointed out and two unconventional presentations are commented on.