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Strong gravitational lensing along with the distance sum rule method canconstrain both cosmological parameters as well as density profiles of galaxieswithout assuming any fiducial cosmological model. To constrain galaxyparameters and cosmic curvature $(\Omega_{k0})$, we use the distance ratio datafrom a recently compiled database of $161$ galactic scale strong lensingsystems. We use databases of supernovae type-Ia (Pantheon) and Gamma Ray Bursts(GRBs) for calculating the luminosity distance. To study the model of the lensgalaxy, we consider a general lens model namely, the Extended Power-Law model.Further, we take into account two different parametrisations of the massdensity power-law index $(\gamma)$ to study the dependence of $\gamma$ onredshift. The best value of $\Omega_{k0}$ suggests a closed universe, though aflat universe is accommodated at $68\%$ confidence level. We find thatparametrisations of $\gamma$ have a negligible impact on the best fit value ofthe cosmic curvature parameter.  Furthermore, measurement of time delay can be a promising cosmographic probevia "time delay distance" that includes the ratio of distances between theobserver, the lens and the source. We again use the distance sum rule methodwith time-delay distance dataset of H0LiCOW to put constraints on the CosmicDistance Duality Relation (CDDR) and the cosmic curvature parameter$(\Omega_{k0})$. For this we consider two different redshift-dependentparametrisations of the distance duality parameter $(\eta)$. The best fit valueof $\Omega_{k0}$ clearly indicates an open universe. However, a flat universecan be accommodated at $95\%$ confidence level. Further, at $95\%$ confidencelevel, no violation of CDDR is observed. We believe that a larger sample ofstrong gravitational lensing systems is needed in order to improve theconstraints on the cosmic curvature and distance duality parameter.

Constraining Cosmological and Galaxy Parameters using Strong Gravitational Lensing Systems