Magnetic properties of high-T[subscript] c superconductors have been studied in order to determine the free-energy surface, the characteristic critical fields, order parameters structure, and the grain size effect on magnetization. Studies of the thermodynamic reversibility for YBa[subscript]2Cu[subscript]3O[subscript]7-[delta] show the rounding in magnetization vs. temperature curves is a reflection of the thermodynamic fluctuations near T[subscript] c. Specific heat jump C(0)-C(H) values that have been calculated from the free-energy surfaces show good agreement with the direct calorimetric measurements;Comparative studies of the free-energy surfaces, flux creep and critical currents for both melt-textured and grain-aligned YBa[subscript]2Cu[subscript]3O[subscript]7-[delta] samples have been undertaken in order to evaluate the difference caused by different micro structures in these samples. The free energy per unit length of a vortex is found to be essentially the same in the melt-textured sample as for the single crystals in the grain-aligned sample, suggesting that the line energy is the same for these rather different samples. The specific heat jump values calculated from the free-energy surfaces also show close agreement between the two samples;Magnetic field and temperature dependence of the average Ginzburg-Landau order parameter \langle f\rangle is evaluated by fitting the magnetization data of grain-aligned YBa[subscript]2Cu[subscript]3O[subscript]7-[delta] to the Hao-Clem model in the region of thermodynamic reversibility. H[subscript] c(T) and H[subscript] c2(T) were also determined from the fitting along with the [kappa][subscript] c(T) values. The study reveals that [kappa][subscript] c is a slowly decreasing function of temperature near T[subscript] c. Fittings of the same model to Bi[subscript]2Sr[subscript]2Ca[subscript]2Cu[subscript]3O[subscript]10 have been carried out. The 2-D nature of bismuth family superconductors introduces some difficulties in applying Hao-Clem model and it is discussed in comparison with YBa[subscript]2Cu[subscript]3O[subscript]7-[delta] results;Lastly, studies on the grain size effect on free energy and specific heat jump in grain aligned YBa[subscript]2Cu[subscript]3O[subscript]7-[delta] samples show that the free energy is reduced by about 15% as the average grain size changes from 37.5 to 12.7 [mu]. The twin spacing d is related to the average grain size D by d∝√D and is thought to be the major factor that causes the decrease in the free energy.