  HC$_3$N is an ubiquitous molecule in interstellar environments, from external
galaxies, to Galactic interstellar clouds, star forming regions, and planetary
atmospheres. Observations of its rotational and vibrational transitions provide
important information on the physical and chemical structure of the above
environments. We present the most complete global analysis of the spectroscopic
data of HC$_3$N. We have recorded the high-resolution infrared spectrum from
450 to 1350 cm$^{-1}$, a region dominated by the intense $\nu_5$ and $\nu_6$
fundamental bands, located at 660 and 500 cm$^{-1}$, respectively, and their
associated hot bands. Pure rotational transitions in the ground and
vibrationally excited states have been recorded in the millimetre and
sub-millimetre regions in order to extend the frequency range so far considered
in previous investigations. All the transitions from the literature and from
this work involving energy levels lower than 1000 cm$^{-1}$ have been fitted
together to an effective Hamiltonian. Because of the presence of various
anharmonic resonances, the Hamiltonian includes a number of interaction
constants, in addition to the conventional rotational and vibrational l-type
resonance terms. The data set contains about 3400 ro-vibrational lines of 13
bands and some 1500 pure rotational lines belonging to 12 vibrational states.
More than 120 spectroscopic constants have been determined directly from the
fit, without any assumption deduced from theoretical calculations or
comparisons with similar molecules. An extensive list of highly accurate rest
frequencies has been produced to assist astronomical searches and data
interpretation. These improved data, have enabled a refined analysis of the
ALMA observations towards Sgr B2(N2).
