Thermodynamics has been studied systematically for the high temperature cuprate superconductor La2-xSrxCuO4-d , La-214, in the entire superconductive region from strongly underdoped to strongly overdoped regimes. Magnetization studies with H∥ c have been made in order to investigate the changes in free energy of the system as the number of carriers is reduced. Above the superconducting transition temperature, the normal-state magnetization exhibits a two-dimensional Heisenberg antiferromagnetic behavior. Below Tc, magnetization data are thermodynamically reversible over large portions of the H-T plane, so the free energy is well defined in these regions. As the Sr concentration is varied over the wide range from 0.060 (strongly underdoped) to 0.234 (strongly overdoped), the free energy change goes through a maximum at the optimum doped in a manner similar to the Tc0 vs. x curve. The density of states, N(0), remains nearly constant in the overdoped and optimum doped regimes, taking a broad maximum around x = 0.188, and then drops abruptly towards zero in the underdoped regime.;The La2-xSrxCuO4 (La-214) system displays the fluctuating vortex behavior with the characteristic of either 2D or 3D fluctuations as indicated by clearly identifiable crossing points T* close to Tc. The dimensional character of the fluctuations depends on both applied magnetic fields and the density of charge carriers. The dimensional crossover from 2D to 3D occurs in the strongly underdoped regime when the c-axis coherence distance xic becomes comparable to the spacing between adjacent CuO2 layers s at sufficiently high magnetic fields near Hc2.