  We consider a member of the family of scalar-tensor theories of Inflation -
the so-called Horndeski model for Inflation, for which we calculate the
non-Gaussianity (NG) and the power spectrum of curvature perturbations. We
concentrate on the determination of the power spectrum, and the bi-spectrum
along with the associated $f_\mathrm{NL}$ parameter and the Spectral Index. We
follow the methodology outlined within the Quantum field theory framework
(S-matrix approach and Weinberg's 'in-in' formalism) and compare - whenever
necessary - our findings with those obtained via the traditional $\delta$N
formalism. The work contained herein is an extensive review of the existing
literature on this subject and the 'Inflationary theory' in general, along with
some newly developed techniques and calculations.
