  Background: The Po, Pb, Hg, and Pt region is known for the presence of
coexisting structures that correspond to different particle-hole configurations
in the Shell Model language or equivalently to nuclear shapes with different
deformation.
  Purpose: We intend to study the configuration mixing phenomenon in the Hg
isotopes and to understand how different observables are influenced by it.
  Method: We study in detail a long chain of mercury isotopes, $^{172-200}$Hg,
using the interacting boson model with configuration mixing. The parameters of
the Hamiltonians are fixed through a least square fit to the known energies and
absolute B(E2) transition rates of states up to $3$ MeV.
  Results: We obtained the IBM-CM Hamiltonians and we calculate excitation
energies, B(E2)'s, quadrupole shape invariants, wave functions, isotopic
shifts, and mean field energy surfaces.
  Conclusions: We obtain a fairly good agreement with the experimental data for
all the studied observables and we conclude that the Hamiltonian and the states
we obtain constitute a good approximation to the Hg isotopes.
