ABSTRACT: Gravity is fundamental to formulate the standard cosmological model and understand smaller-scale astrophysical processes. This thesis studies different problems involving weak and strong gravitational effects in astrophysics and cosmology. In the strong gravity regime, we use a neural network to reconstruct the parameters of a binary black hole merger from its gravitational wave signal. Effective one-body numerical relativity simulations are used to generate a template bank of gravitational waves spectrograms. This dataset is then used to train a neural network to estimate the masses of the black holes. In the weak gravity regime, we study static spherically symmetric (SSS) metrics as generalizations of the de Sitter metric and find their form as perturbations of the FRW Universe using gauge-invariant variables. We then apply these results to compute the turnaround radius (TAR) and the gravitational stability mass (GSM) to constrain scalar-tensor gravity theories with observational data. In the last part, we investigate the problem of reconstructing the density field from its weak lensing effects on the luminosity distance. First, we simulate many random configurations of cosmic structure, compute their effects on the luminosity distance using perturbation theory, and finally develop a neural network to reconstruct the density and velocity fields from the luminosity distance.