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In this book, we are interested to discuss various Astrophysical and Cosmological problem within the frame work of Numerical relativity. We fitted the rotational velocity curve by using spline interpolation method based on the experimental data and further explored other properties of wormhole by using Einstein field equation. This result provides a clue for possible existence of wormhole in most of the galaxies and provides a theoretical platform to seek observational evidence for wormholes by studying the scattering of scalar waves. In another study, we used a proportionate functional form of rotational velocity and regain the wormhole property in a reverse manner. We also investigated the possibility of existence of wormhole by the help of some well-known properties of using different density profiles. We also look into the lensing effect of Electro-magnetic charged blackhole. We calculate the de_ection angle due to bending of light in the region outside the event horizon of an electromagnetic charged black hole deriving the analytical expression of gravitational time delay. We evaluated numerically the de_ection angle and the time delay between different relativistic images.