The current status of the recent developments of the second-order
gauge-invariant cosmological perturbation theory is reviewed. To show the
essence of this perturbation theory, we concentrate only on the universe filled
with a single scalar field. Through this review, we point out the problems
which should be clarified for the further theoretical sophistication of this
perturbation theory. We also expect that this theoretical sophistication will
be also useful to discuss the theoretical predictions of Non-Gaussianity in CMB
and comparison with observations.Comment: 26 pages, 2 figures, Summary report on the current status of the
second-order gauge-invariant cosmological perturbation theory, Published as
an invited review in the Special Issue "Testing the Gaussianity and
Statistical Isotropy of the Universe" in Advances in Astronom
