  The Rotar central limit theorem is a remarkable theorem in the non-classical
version since it does not use the condition of asymptotic infinitesimality for
the independent individual summands, unlike the theorems named Lindeberg's and
Lindeberg-Feller's in the classical version. The Rotar central limit theorem
generalizes the classical Lindeberg-Feller central limit theorem since the
Rotar condition is weaker than Lindeberg's.
  The main aim of this paper is to introduce the Rotar central limit theorem
for sums of a random number of independent (not necessarily identically
distributed) random variables and the conditions for its validity. The order of
approximation in this theorem is also considered in this paper.
