  In this paper, we give rates of convergence, for minimal distances and for
the uniform distance, between the law of partial sums of martingale differences
and thelimiting Gaussian distribution. More precisely, denoting by $P_{X}$ the
law of a random variable $X$ and by $G_{a}$ the normal distribution ${\mathcal
N} (0,a)$, we are interested by giving quantitative estimates for the
convergence of $P_{S_n/\sqrt{V_n}}$ to $G_1$, where $S_n$ is the partial sum
associated with either martingale differences sequences or more general
dependent sequences, and $V_n= {\rm Var}(S_n)$. Applications to linear
statistics, non stationary $\rho$-mixing sequences and sequential dynamical
systems are given.
