  We construct the gravity dual of three-dimensional, $SU(N_{\textrm{c}})$
super Yang-Mills theory with $N_{\textrm{f}}$ flavors of dynamical quarks in
the presence of a non-zero quark density $N_{\textrm{q}}$. The supergravity
solutions include the backreaction of $N_{\textrm{c}}$ color D2-branes and
$N_{\textrm{f}}$ flavor D6-branes with $N_{\textrm{q}}$ units of electric flux
on their worldvolume. For massless quarks, the solutions depend non-trivially
only on the dimensionless combination $\rho=N_{\textrm{c}}^2 N_{\textrm{q}} /
\lambda^2 N_{\textrm{f}}^4$, with $\lambda=g_{\textrm{YM}}^2 N_{\textrm{c}}$
the 't Hooft coupling, and describe renormalization group flows between the
super Yang-Mills theory in the ultraviolet and a non-relativistic theory in the
infrared. The latter is dual to a hyperscaling-violating, Lifshitz-like
geometry with dynamical and hyperscaling-violating exponents $z=5$ and
$\theta=1$, respectively. If $\rho \ll 1$ then at intermediate energies there
is also an approximate AdS$_4$ region, dual to a conformal Chern-Simons-Matter
theory, in which the flow exhibits quasi-conformal dynamics. At zero
temperature we compute the chemical potential and the equation of state and
extract the speed of sound. At low temperature we compute the entropy density
and extract the number of low-energy degrees of freedom. For quarks of non-zero
mass $M_{\textrm{q}}$ the physics depends non-trivially on $\rho$ and
$M_{\textrm{q}} N_{\textrm{c}}/\lambda N_{\textrm{f}}$.
