In order to make some improvements in density functional theory, we have proposed the composite effective potential method. This method creates a density for the system in compliance with the exact ground-state density. We start with known experimental or extremely accurate theoretical values for(' ),(' )then we create the composite effective potential,(' )U('c)(r), which is a linear superposition of effective potentials of a group of isoelectronic(' )systems. Each potential is multiplied by some selected parameter to give the desired effective potential. This effective potential is substituted for the effected potential of the system derived from the local spin density approxi-mation. The parameters should be varied until <1/r) is obtained exactly. In a separate step similar to the self-interaction correction, we subtract a small term from the exchange-correlation potential of the local spin density approximation. In both steps, we have extensively studied the helium-like ions. Also, we have extended our study to some larger systems such as neon. In a separate chapter, we suggest the addition of an inhomogeneity correction to the Thomas-Fermi kinetic energy model. From this new form, we derive a simple gradient expansion. This extension includes the Thomas-Fermi term{6-7}, the Weizsacker term{10}, and the most significant term of Hodges{12}. The same method is applied to the exchange energy functional. The results resemble the well known expansion{16-17} but differ only in the numerical coefficients