Density Functional Theory (DFT) was used to study fundamental characteristics of electrides. Electronic structure calculations were performed with the generalized gradient approximation (GGA) and GGA+U (U- “on-site" electron-electron repulsion). Fundamental properties of Y2C were investigated in the first project. The nature of strongly localized anionic electrons in Y2C was demonstrated using the distribution of charge density. Magnetic properties were analyzed with magnetization density and magnetic anisotropy energies. The magnetic anisotropy of Y2C originates from anionic electrons at interlayer spaces. The predicted work functions are in good agreement with reported experimental data. We also investigated the enhancement of magnetic properties by varying the degree of localization of anionic electrons. The exchange splitting of interstitial electrons is more prominent than that of d-orbitals of Y and exchange splitting increases with decreasing c-axis parameter. In the second study, fundamental properties of Gd2C are discussed. The GGA+U method was applied for 4f states of Gd and predicted the best U value. Our model predicted Gd2C has a layered-hexagonal structure. Local density of states (LDOS) and projected density of states (PDOS) were analyzed for understanding of anionic electrons and atoms on magnetic and electronic properties. The Curie temperatures of Gd and Gd2C were calculated and noticed that interactions in Gd2C are influential to increase the Curie temperature. The chemical formula can be written as [Gd2C]1.9.1.9e- from charge analysis. Additionally, fundamental properties of two ionized states, Q=+1 and Q=+2 were studied. Results indicate anionic electrons at interlayer spaces will initiate the ejecting of electrons. Density functional perturbation theory (DFPT) with DFT under the harmonic approximations was applied to study the structural stabilities, phase transitions and variation of thermodynamic quantities at finite temperature of two phases of Hf2S. Phonon dispersion curves without any imaginary frequencies are evidence for stability of two phases. The resulting quadratic flexural phonon branch indicates Hf2S has 2D characteristics. At T= 0 K the Helmholtz free energy of anti- NbS2 structure of Hf2S lies ≈23 kJ/f.u. below that of the higher energy phase. The critical temperature for the phase transition was estimated, and the effect of finite temperature on thermodynamics quantities were studied.