Introduction to Lie Algebras and Their Representations

This paper is made up of a desire for me to contribute to this beautiful field of mathematics that I have encountered in recent years. In addition, I would like to mention that I am not aware that there are papers in our Balkans on Lie algebra, although this is only an introductory part for which in the near future in collaboration with several professors from abroad I will do a book in our mother tongue on Lie groups and algebras. The main content of this paper is similar to the books that have been published regarding Lie algebras, from basic definition and example, structure, killing form, classification to root system. In my opinion, this paper is important in relation to Lie algebras, because it will be helpful to all those who write papers on algebra, as well as the fact that the paper will be written in Montenegrin, which is understood by almost more than 70 percent of the population. For me, this work has the significance of being useful to all who need it.