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This article is intended to people interested in electromagnetic high-frequency diffraction by perfectly and imperfectly conducting objects. It describes the physical foundations and postulates of the Geometrical Theory of Diffraction as formulated originally by Keller. A great emphasis is devoted to the mathematical foundations of the theory which permits to elucidate its possibilities and limitations and to introduce later developments and improvements (See Part II of this article). For each diffraction process, the most important formulas of GTD are presented with comments concerning their utility in practical applications and a review of available diffraction coefficients.