Abstarct: The excellent electronic and optical properties of wide band gap Tin oxide, makes it exciting material for technological applications. Doped in SnO2 with transition mextals, make it suitable for using in spintronic devices. In this thesis, the structural, electronic, magnetic and optical properties of pure Tin oxide and doped with Co, Fe and Mn, were investigated using WIEN2k code. In calculations, we used the local density approximation (LDA) and generalized gradient approximation (GGA), for pure Tin oxide, and the GGA, for doped structures. The study of partial density of states of Tin oxide revealed, the coupling states is originated from hybridization between O 2p and Sn 5s, and also hybridization between O 2p and Sn 5p. The study of the partial density of states of the Tin oxide doped with transition mextals revealed that the most contribution in the density of states, near the Fermi level in the valence band and conduction band are mainly from TM-3d. The TM doped compounds indicated that for concentration of 12.5% Co and Fe, when two magnetic ions are close to each others, the stable phase is ferromagnetic and for Mn doped SnO2, is antiferromagtetic. It is also determined, for concentration of 12.5% Fe and Mn, in the case of two magnetic ions are far away, the stable phase is antiferromagtetic. For concentration of 25%, the stable magnetic phase for Co, Fe and Mn, is ferromagnetic. The results of the optical spectrum calculations showed, with increase in dopant concentration, the intensity of the first peak in the absorption diagram increases and the intensities of the other picks decrease. Also with increasing of dopant concentration to 12.5%, the absorption spectra of Sn1-xTMxO2 samples, show a red shift, and for higher concentrations, depending on the type of the TM element, red shift or blue shift was observed.