In this work, we present the heteroepitaxial and homoepitaxial growth and characterization of single crystal Ga2O3 by plasma-assisted molecular beam epitaxy (MBE). For growth, flux-temperature measurements were done on Ga, In, and Sn cells to find the appropriate temperature for a specific beam equivalent pressure (BEP). In the first set of experiments, (201) and (100) Ga2O3 thin films were grown on c-plane (001) sapphire and (100) 􀀀Ga2O3 substrates, respectively. Samples were grown at a constant oxygen flux of 1.5e-􀀀5 (Torr) and substrate temperature of 700C. Four different gallium fluxes (2e-􀀀8, 5e-8, 8e-8, and1.1e-7 (Torr)) were investigated. Optical spectroscopy, atomic force microscopy (AFM), scanning (SEM); transmission electron microscopy (TEM), and xray diffraction (XRD) were done on samples. The characterizations showed lower growth rate at higher gallium fluxes and smoother surfaces at lower gallium fluxes for both heteroepitaxy and homoepitaxy. In the next step, different dopants (Si, In, and Sn) were studied for doping. Data analysis showed successful incorporation of Si atoms in Ga2O3 crystal structure. However, further investigations revealed that Si atoms did not act as dopants. On the other hand, Ga2O3 could be doped n-type with Sn. Also, Ga2O3 thin films could be successfully delta-doped by Sn. While GaSnO/Ga2O3 heterostructures could be successfully grown on (001) sapphire substrate by alloying of Sn into Ga2O3 crystal structure, InGaO/Ga2O3 could not be achieved due to non-uniform distribution of In inside the Ga2O3 crystal.