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.