  The dark matter haloes associated with galaxies have hitherto established
strong correlations within a range of observed parameters, known as scaling
relations of dark matter haloes. The origin of these scaling relations still
contains significant ambiguities and requires comprehensive exploration for
complete understanding. Utilising the correlation between the concentration and
mass of dark matter haloes inferred from cosmological $N$-body simulations
based on the cold dark matter paradigm ($c$-$M$ relation), we derive
theoretical scaling relations among other physical quantities such as the
surface mass density, the maximum circular velocity, and the scale radius of
the dark matter halo. By comparing theoretical and observed scaling relations
at various mass scales, it is found that the scaling relations observed in
dwarf galaxies and galaxies originate in the $c$-$M$ relation of the dark
matter halo. We predict that this theoretical scaling relation is also
established in galaxy clusters. Moreover, we propose a novel theoretical
scaling relation that incorporates the effects of the cusp-to-core transition,
which is supposed to occur in cold dark matter haloes. Our discussion concludes
with the exploration of potential observational verification of the
cusp-to-core transition process in dark matter haloes.
