  We study the gauge invariant cosmological perturbations up to second order.
We show that there are infinite families of gauge invariant variables at both
of the first and second orders. The conversion formulae among different
families are shown to be described by a finite number of bases that are gauge
invariant. For the second order cosmological perturbations induced by the first
order scalar perturbations, we explicitly represent the equations of motion of
them in terms of the gauge invariant Newtonian, synchronous and hybrid
variables, respectively.
