Abstract
This chapter discusses the peculiarities in the development of the theory of Lie groups. This subject is highly developed and very well-documented. The main facts about its history can be found by simply tracing back the references, usually published in the top journals of the time. In some cases, the present-day terminology is even quite wrong. However, the terminology is not changed because it is already too deeply engrained. Also, the facts are known to most experts, so there is no pretence to have discovered anything new. A Lie algebra is called simple if it has no nontrivial ideals. The term semisimple is introduced for a Lie algebra that is equal to the direct sum of non-abelian simple Lie algebras. Earlier, it was thought that there were no other simple Lie algebras than those of the special linear and the orthogonal groups. The theory of Lie groups has always had a strong geometric flavor.
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