High temperature superconductivity is a remarkable phenomenon in which certain materials conduct electricity with zero electrical resistance and expel an internal magnetic field at temperatures higher than 30 K. Bednorz and Muller discovered this phenomenon in copper oxide compounds. Following this finding, researchers continued looking for new high-temperature superconducting families, which is still going on. Superconductivity and magnetism were formerly assumed to be mutually exclusive until the discovery of several rare earth ternary compounds that demonstrate their coexistence. Layered superconductivity and magnetism coexist in several of the recently found iron-based materials. By establishing a compressive model and generic equations, the major goal of this research work is to examine the nature of high-temperature superconductivity in a two-band model for Na and Ni doped BaFe2As2 iron-based superconductors. By developing a model Hamiltonian for the system and using quantum field theory Green's function formalism and phenomenological Ginzburg-Landau (GL) free energy density functional theory in a two-band model, we obtained the expression for the superconducting order parameters, superconducting transition temperature, density of states, electronic specific heat, entropy, condensation energy, the possible coexistence of superconductivity and spin density wave (SDW), the upper critical magnetic field (HC2), Ginzburg-Landau coherence length ( ) and Ginzburg-Landau penetration depth ( ). Besides, the effects of electron and hole intra-band superconducting pairing interactions, as well as the inter-band pair interaction between the two bands in the two-band model in the Bardeen, Cooper, and Schrieffer (BCS) mean field approximation for Na and Ni doped BaFe2As2 superconductor, have been studied in this dissertation. Phase diagrams of superconducting order parameter ( ) versus temperature, density of state versus temperature, electronic specific heat versus temperature, entropy versus temperature, and condensation energy versus temperature have been plotted for all bands using the obtained expressions. The effect of all intra-inter band pairings on the total superconducting order parameters at zero temperature is 17 meV, and demonstrates the contribution of combined intra-inter band pairing in the two-band model on strengthening the pairing mechanism of high-temperature superconductors. Parameterization of High Temperature Superconductivity xv We have also found a mathematical expression for the relationship between the superconducting transition temperature (TC) and the inter-band pairing potential (Ueh), as well as the relationship between density of states and excitation energy and temperature, and plotted their phase diagrams. In addition, we are curious to observe whether the transition between the two states is first order or the two pure phases are separated by an intermediate phase with superconductivity and SDW orders coexisting. In the same way, phase diagrams of TC versus in the electron and hole intra-bands, as well as in the inter-band, are plotted using the experimental and the theoretical values of the parameters in the generated equations. The phase diagram of spin density wave transition temperature (TSDW) versus spin density wave order parameter ) is depicted using the obtained equations for the spin density wave transition temperature (TSDW) dependency on the spin density wave order parameter ( ). The possibility of the coexistence of superconductivity and spin density wave (SDW) in the two-band model of Ba1-xNaxFe2As2 is demonstrated by merging the two-phase diagrams. Finally, we have investigated the upper critical magnetic field (HC2), Ginzburg-Landau coherence length ( ), and Ginzburg-Landau penetration depth ( ) in a two-band model of Na and Ni doped BaFe2As2 iron-based superconductors. The phase diagrams for the temperature dependence of upper critical magnetic fields parallel and perpendicular to the crystallographic c axis versus temperatures for our considered system are displayed in the same way, using the experimental values in the obtained equations. The temperature dependence of GL coherence lengths, penetration depths, and the characteristics parameters in the ab-plane, and along the c axis versus temperature are plotted using the obtained expressions. We showed that the upper critical magnetic field along the ab-plane is greater than along the crystallographic c-axis, and thus our iron-based superconductor has higher upper critical magnetic field values. In general, we presented a framework for understanding some of the universal features of high temperature iron-based superconductors in the current work. The conclusions of this study are in a broad agreement with prior experimental findings. Parameterization of High Temperature Superconductivity xvi Keywords: High-temperature superconductivity, iron-based superconductors, Ba1-xNaxFe2As2, Ba(Fe1-xNix)2As2, two-band model, Green‟s function, Ginzburg-Landau theory, order parameters( ), density of states(DS), electronic specific heat (Ces), entropy(S), condensation energy(EC), spin density wave, coexistence of superconductivity and spin density wave, upper critical magnetic field(HC2), GL coherence length(ӠGL), GL penetration depth(λGL).