The most intriguing aspect of studying supernovae associated with gamma-ray bursts (GRB-SNe) is the fact that they are accompanied by the most energetic events in the universe: gamma-ray bursts (GRBs). GRBs are extremely bright, which makes a swift trigger of observation on them. Therefore, a supernova (SN) light curve following a GRB can be detected. In addition, GRB-SN rate does not decline beyond z > 1:5, which is a fundamental feature to breakdown degeneracies in the constraint on the equation of state parameter w(z). Apart from two exceptions, i.e., GRB 060614 and GRB 060505, all other long GRBs have been observed followed by a SN. Hundreds of GRBs are detected yearly though, properties and progenitor mechanism of GRB-SNe remain elusive, due to the difficulties in obtaining the light curves of GRB-SNe. For example, the brightness of a GRB and a host galaxy may conceal a GRB-SN, and dust in the line of sight may also blur the brightness of a GRB-SN. In this thesis, supernovae (SNe), especially GRB-SNe are extensively explored and used as a tool to study the dark distant universe. We first intend to estimate the rates of observing a lensed SN behind Abell 1689. A function describing time delay distribution of strong gravitational lensing is developed. For Type Ia supernova (SNe Ia), the rate is lower than core-collapse supernovae (CC SNe). The rate of SNe Ia declines beyond z 1:5. Based on these reasons, we investigate a potential candidate to measure cosmological distance: GRB-SNe. They are a subclass of CC SNe. Light curves of GRB-SNe are obtained and their properties are studied. We ascertain that the properties of GRB-SNe make them another candidate for standardizable candles in measuring the cosmic distance. Cosmological parameters M and are constrained with the help of GRB-SNe. The first Chapter presents a theoretical background of this thesis divided into three Sections. In the first Section, a theory of gravitational lensing is briefly introduced. The lensing effects are strongly depended on the mass distribution of a lensing cluster. We discussed models of mass distributions of a cluster of galaxies. We also theoretically deduce time delay. The second Section is dedicated to SN. Progenitor models of different types of SNe are investigated. SNe Ia and their application as standard candles are discussed.