  Using a new powerful technique based on the notion of megaideal, we construct
a complete set of inequivalent realizations of real Lie algebras of dimension
no greater than four in vector fields on a space of an arbitrary (finite)
number of variables. Our classification amends and essentially generalizes
earlier works on the subject.
  Known results on classification of low-dimensional real Lie algebras, their
automorphisms, differentiations, ideals, subalgebras and realizations are
reviewed.
