Karatsuba's method of estimating of short Kloosterman sums

In the middle of 1990th, A.A. Karatsuba invented a new and original method of estimating of short Kloosterman sums, that is, the exponential sums of the folloving type:
$$ S(m,A)=\sum_{n\in A}\exp{\biggl(\frac{an^{*}+bn}{m}\biggr)},\quad nn^*\equiv 1 \pmod m. $$
Here $m>2$, $A$ denotes some subset of reduced residual system $\mathbb{Z}_{m}^{*}$ modulo $m$, such that its cardinality $|A|$ does not exceed arbitrary small fixed power of $m$. In the talk, we will discuss the last results concerning such sums and the further development of Karatsuba's method.