In this thesis, we give an introductory account of inflationary cosmology. We explain how a period of accelerated expansion in the Universe’s early stages can explain some paradoxes encountered in cosmology. Furthermore, we study the quantum fluctuations of a generic scalar field during inflation while putting the emphasis on the different behaviour of the fluctuations in or out of the horizon. Finally, we consider an inflationary potential composed of two coupled scalar fields: one flat direction and a non-flat one. We solve the Langevin equations numerically for these two fields and contrast our results and approach with two previous studies. We find that the fluctuations of the flat direction does not saturate in the range of e-folds considered.