  We give a proof of the $A_2$ conjecture in geometrically doubling metric
spaces (GDMS), i.e. a metric space where one can fit not more than a fixed
amount of disjoint balls of radius $r$ in a ball of radius $2r$. Our proof
consists of three main parts: a construction of a random "dyadic" lattice in a
metric space; a clever averaging trick from [3], which decomposes a "hard" part
of a Calderon-Zygmund operator into dyadic shifts (adjusted to metric setting);
and the estimates for these dyadic shifts, made in [16] and later in [19].
