Lagrangian Perturbation Theory (LPT) is a powerful method to model nonlinear evolution of large scale structure analytically. This thesis investigates the convergence properties of this theory by applying it to a simple test problem the spherical top-hat. The method of Largangian re-expansions is introduced to improve the convergence properties of the series. This method involves reexpanding the solution in overlapping time domains, each domain subject to a time of validity criteria. The results show that there is a trade-off between the Lagrangian order and number of steps; one can achieve the same accuracy with a lower order scheme and more time steps as that with a higher order scheme and a single step. The method developed based on the top-hat is then applied to model evolution of inhomogeneous initial conditions. A numerical code is developed and tested. Tests of convergence with Lagrangian order, step size and grid size are presented.