In this talk, the results of student's research project concerning realizations of Lie algebras
will be presented. Realizations of Lie algebras play an important role mainly in the theory of
differential equations. By a realization, we mean a representation of the Lie algebra structure
by vector fields. One of the natural problems is the classification of all realizations of a given
Lie algebra. We will show how classification of so called transitive realizations corresponds to
classification of subalgebras and how these transitive realizations can be easily explicitly
computed by a method based on work of I. V. Shirokov et al. We use this method for construction
of realizations of five-dimensional Lie algebras.