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In the paper we are going to analyze the most important from our viewpoint mathematical and physical ambiguities in the generally accepted classical (not quantum) field theory. The instantaneous action at a distance in classical electrodynamics is discussed. The meanings of Pointing and Umov vectors are clarified. Some important remarks concern interactions and causality. Problems, connected with different gauge invariances in electrodynamics, are considered in detail. Parametric transformation of Galileo is suggested. Aberration of light is analyzed. Different mappings and the curvature of space are discussed.