  In this paper we report the results of the first $\sim$four years of
spectroscopic and photometric monitoring of the Type IIn supernova SN 2015da
(also known as PSN J13522411+3941286, or iPTF16tu). The supernova exploded in
the nearby spiral galaxy NGC 5337 in a relatively highly extinguished
environment. The transient showed prominent narrow Balmer lines in emission at
all times and a slow rise to maximum in all bands. In addition, early
observations performed by amateur astronomers give a very well-constrained
explosion epoch. The observables are consistent with continuous interaction
between the supernova ejecta and a dense and extended H-rich circumstellar
medium. The presence of such an extended and dense medium is difficult to
reconcile with standard stellar evolution models, since the metallicity at the
position of SN 2015da seems to be slightly subsolar. Interaction is likely the
mechanism powering the light curve, as confirmed by the analysis of the pseudo
bolometric light curve, which gives a total radiated energy
$\gtrsim10^{51}\,\rm{erg}$. Modeling the light curve in the context of a
supernova shock breakout through a dense circumstellar medium allowed us to
infer the mass of the prexisting gas to be $\simeq8\,\rm{M_{\odot}}$, with an
extreme mass-loss rate for the progenitor star
$\simeq0.6\,\rm{M_{\odot}}\,\rm{yr^{-1}}$, suggesting that most of the
circumstellar gas was produced during multiple eruptive events. Near- and
mid-infrared observations reveal a flux excess in these domains, similar to
those observed in SN 2010jl and other interacting transients, likely due to
preexisting radiatively heated dust surrounding the supernova. By modeling the
infrared excess, we infer a mass $\gtrsim0.4\times10^{-3}\,\rm{M_{\odot}}$ for
the dust.
