  The aim of this paper is to prove a trace theorem for Besov functions in the
metric setting, generalizing a known result from A. Jonsson and H. Wallin in
the Euclidean case. We show that the trace of a Besov space defined in a `big
set' $X$ is another Besov space defined in the `small set' $F\subset X$. The
proof is divided in three parts. First we see that Besov functions in $F$ are
restrictions of functions of the same type (but greater regularity) in $X$,
that is we prove an Extension theorem. Next, as an auxiliary result that can
also be interesting on its own, we show that the interpolation between certain
potential spaces gives a Besov space. Finally, to obtain that Besov functions
in $X$ can in fact be restricted to $F$, a Restriction theorem, we first prove
that this result holds for functions in the potential space, and then by the
interpolation result previously shown, it must hold in the Besov case. For the
interpolation and restriction theorems, we make additional assumptions on the
spaces $X$ and $F$, and on the order of regularity of the functions involved.
