  This paper is concerned with Mahler's method. We study in detail the
structure of linear relations between values of Mahler functions at algebraic
points. In particular, given a field ${\bf k}$, a Mahler function $f(z)\in{\bf
k}\{z\}$, and an algebraic number $\alpha$, $0<\vert \alpha\vert <1$, that is
not a pole for $f$, we show that one can always determined whether the number
$f(\alpha)$ is transcendental or not. In the latter case, we obtain that
$f(\alpha)$ belong to the number fields ${\bf k}(\alpha)$. We also consider
some consequences of such results to a classical number theoretical problem:
the study of sequences of digits of algebraic numbers in an integer (or, more
generally, algebraic) base. Our results are based on a theorem of Philippon
[31] that we refine. We also simplify his proof.
