The proposed book is devoted to a systematic analysis of the classical theory of electromagnetic phenomena. Some incorrectnesses for the application of mathematics in theoretical physics are discussed. Many controversial and insufficiently substantiated moments of the classical theory of electromagnetism are analyzed in detail: its foundations, interpretations, mathematical methods and consequences. The book contains an analysis of a number of electrodynamical experiments. All this shows the insufficient validity of the theory of electromagnetic phenomena and the need for serious work on its foundation. Also, the book discusses some alternative ideas related to electromagnetic phenomena. This book can be useful for students, graduate st...