In this thesis, the La 0.5 Ca 0.5 Mn 1-x Co x O 3 (0?x?0.25) micrometer and nanometer sized samples were synthesized by a simple method which is based on the solid state ball-milling and calcinations of acetate and nitrate precursors in the presence of citric acid and their structural, magnetic and electrical properties have been investigated. Reitveld refinement of X-ray diffraction patterns indicates an orthorhombic structure with Pnma space group for all the samples. In all samples with 1350 o C (S1350, micrometer sized samples) and 800 o C (S800, nanometer sized samples) sintering temperatures, the unit cell volume doesn’t change regularly with Co content in 0?x?0.025 samples, but it extremely decreases by further increase in Co doping level up to x=0.05. Since the average ionic radius of Mn av (0.585 ?) is between the ionic radius of Co 2+ (0.65 ?) and Co 3+ (0.55 ?), it can be assumed that Co ions exist in the form of Co 2+ and Co 3+ in these samples and the charge redistribution of Mn 3+ +Co 3+ ?Mn 4+ +Co 2+ occurs for 0?x?0.025 samples. In contrast, by further increase in Co doping level, the charge redistribution weakened, so the most of Co ions appear in the form of Co 3+ in samples. The drastic reduction of unit cell volume in x=0.05 sample, also can be explained on the basis of appearance and increase of Co 3+ ions which are smaller than Mn av ones. FE-ESM images confirm formation of micrometer and nanometer particles for S1350 and S800 samples respectively. In S1350 samples, the magnetization (M) and effective magnetic moment (µ eff ) increase initially by increasing x up to x=0.025 and after that they decrease by further increase in x for x=0.05. The ac magnetic susceptibility measurements show that in all S1350 samples, the charge ordering state is suppressed by increasing x. The low doping S1350 samples have thermal hysteresis because of the coexistence of FM and AFM phases and phase separation. Also, we report a feature of thermal hysteresis behavior in La 0.5 Ca 0.5 Mn 1-x Co x O 3 series, which is the inverted thermal hysteresis loop for 0.0075?x?0.05 samples. The notable point of this study is the ability of a small amount of Co doping (0.5 %) to induce insulator-metal transition in the insulating undoped sample at low temperatures in S1350 compounds. The ac susceptibility measurements of S800 compound indicate that all these samples have PM-FM transition with no charge ordering state. Also all of these samples show insulator-like behavior.