  Hydrodynamics, a term apparently introduced by Daniel Bernoulli (1700-1783)
to comprise hydrostatic and hydraulics, has a long history with several
theoretical approaches. Here, after a descriptive introduction, we present
so-called mesoscopic hydro-thermodynamics, which is also referred to as
higher-order generalized hydrodynamics, built within the framework of a
mechanical-statistical formalism. It consists of a description of the material
and heat motion of fluids in terms of the corresponding densities and their
associated fluxes of all orders. In this way, movements are characterized in
terms of intermediate to short wavelengths and intermediate to high
frequencies. The fluxes have associated Maxwell-like times, which play an
important role in determining the appropriate contraction of the description
(of the enormous set of fluxes of all orders) necessary to address the
characterization of the motion in each experimental setup. This study is an
extension of a preliminary article: Physical Review E \textbf{91}, 063011
(2015).
