Primordial non-Gaussianity in Horndeski-type model for Inflation

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.