The analysis of the original issues of the approaches to Lorentz transformations derivation witnesses that they had an evolutionary character which was connected with their applications to the different physical systems and mediums possibilities extensions. In this issue, through the analysis of mathematical methods which were applied while deriving the Lorentz transformations, four major directions which dominated in the first part of the 20th century are investigated. We have pointed out four founders of these directions:
- coordinate approach (V. Voight, G. Fitzgerald, J. Larmor, A. Poincaré, H. Lorentz, A. Einstein, I. Kordysch);
- group approach (H. Minkowski, A. Poincaré, V. Varicak);
- tensor approach (Einstein, Ivanickaya);
- matrix approach (H. Minkowski, A. Poincaré).
The main peculiarities are shown of these approaches and their realizations, through examples of European scientists’ works.
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