In this thesis we have calculated electronic structure of 2D-GaAs within the firstrnprinciples using Quantum ESPRESSO pacakage. We optimized lattice constantrnand identified the nature and values of band gap of Zinc Blende structure galliumrnaresnide (GaAs). Norm-conserving pseudopotential is used for the self-consistentrncalculation, and the Generalized Gradient Approximation (GGA) for the exchangerncorrelation. An optimum lattice constant of 7.4Ã…, 6.1Ã…, and 5.7Ã…, respectively, isrnobtained for 1D, 2D, and 3D, and in close agreement with the experimental valuern5.65Ã…. 2-D GaAs is known to have a gap of 1.8 eV which is in close agreement withrnprevious observations [45], but has 25.9 % error to the experimental value 1.43 eVrn[42]. This work clearly explains that lattice constant increases with decrease inrncrystal size. Moreover, we could identify the charge transfer between the Ga andrnAs atoms. Generally we could make calculations and compare with its 1-D and 3-Drnstructures results.