  We construct the general first-order hydrodynamic theory invariant under time
translations, the Euclidean group of spatial transformations and preserving
particle number, that is with symmetry group
$\mathbb{R}_t\times$ISO$(d)\times$U$(1)$. Such theories are important in a
number of distinct situations, ranging from the hydrodynamics of graphene to
flocking behaviour and the coarse-grained motion of self-propelled organisms.
Furthermore, given the generality of this construction, we are are able to
deduce special cases with higher symmetry by taking the appropriate limits. In
this way we write the complete first-order theory of Lifshitz-invariant
hydrodynamics. Among other results we present a class of non-dissipative first
order theories which preserve parity.
