  In the present paper, we generalize some of the results on Kloosterman sums
proven in \cite{BG} for prime moduli to general moduli. This requires to
establish the corresponding additive properties of the reciprocal set $$
I^{-1}=\{x^{-1}:\quad x\in I\}, $$ where $I$ is an interval in the ring of
residue classes modulo a large positive integer. We apply our bounds on
multilinear exponential sums to the Brun-Titchmarsh theorem and the estimate of
very short Kloosterman sums, hence generalizing our earlier work to the setting
of general modulus.
