This thesis aims to construct Big Bang models and to investigate their properties. Under the warped product spacetime ansatz, we classify all the physical Big Bang models that are spatially homogeneous and analyze their asymptotes. Furthermore, we prove that the Big Bang models with a positive blowup time $r_{\ast}>0$ are dynamically unstable under non-homogeneous perturbations in Chapter 3.In addition, we also prove the stability of specially relativistic fluids on a fixed Big Bang spacetime in Chapter 4. This work implies that Euler equations are not sufficient to generate shocks. One needs the feedback from fluids to metrics, together forming Einstein-Euler equations, to generate shocks.Finally, we prove the global existence of the membrane equation on $\mathbb{R}^{1,2}\times \mathbb{T}^1$ for sufficiently small, compactly supported initial data in Chapter 5. This is a work independent of the previous ones. We use the standard vector field method to show that the energy remains small throughout the time, estabilishing the global existence for the equation.
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