Type Ia Supernovae (SNe) have been used to discover the accelerated expansion of the universe but many open questions remain unanswered. These include the stellar progenitor, extinction and possible systematic trends in the supernova brightness for different host galaxy environments or cosmic time. In this thesis we attempt to address these open questions by looking at a large homogeneous sample of nearby SNe from the Palomar Transient Factory (2009-2012) and the intermediate Palomar Transient Factory (2013-2017) for which we have 265 well-observed light-curves in the R-band and 2981 spectra from a total of 2060 SNe.

In Paper I we study the global properties of the R-band light-curves, such as rise-time, stretch and intrinsic brightness at different SN phases, to examine if there are multiple populations in any of the parameters suggesting different progenitor channels. We do not find evidence supporting this. We characterize the second maximum in the R-band in Paper II and find a correlation between the time from light-curve maximum, and the "colour-stretch" parameter, a proxy for ⁵⁶Ni mass. We also found that the integrated flux under the second maximum, correlates with the transparency timescale, a proxy for total ejecta mass. Using these two relations we find that sub-Chandrasekhar double detonation models can account for the biggest fraction of the PTF/iPTF SNe light-curves properties. In Paper III we present the spectroscopic sample of PTF/iPTF and using automatic machine learning tools to explore spectral features and possible connection to photometric and host galaxy properties.

Paper IV focuses on a small sample of SNe, with multi-wavelength light-curves, to address one of the most important systematic uncertainties in supernova cosmology: extinction by dust in the line-of-sights. We found a diversity in the reddening laws as characterised by the total-to-selective extinction, R_V. Finally, Paper V looks at a strongly lensed SNIa at z=1.4  to see if there is evolution of its spectral and photometric properties over cosmic time. Both Paper IV and Paper V use the code developed for Paper III to analyse spectra.