  Let $\Theta$ be a point in ${\bf R}^n$. We split the classical Khintchine's
Transference Principle into $n-1$ intermediate estimates which connect
exponents $\omega_d(\Theta)$ measuring the sharpness of the approximation to
$\Theta$ by linear rational varieties of dimension $d$, for $0\le d \le n-1$.
We also review old and recent results related to these $n$ exponents.
