In this thesis, synthesis, structural and magnetic properties of the undoped and copper doped cerium oxide nanoparticles have been investigated. The nanoparticles were prepared by sol-gel preparation method. Undoped samples were prepared with different particles sizes by annealing the as-prepared sample at different temperatures Ta = 200°C, 400°C, 550°C, 700°C, 800°C. The particle size varied from 3 nm to 42 nm with increasing annealing temperatures. Copper was doped into CeO2 by annealing the samples at 400°C in ultra high pure nitrogen. The nominal percentages of copper in doped cerium oxide were 2.5%, 5%, 7.5% and 10%.;Structural characterization of the nanoparticles was done using transmission electron microscope (TEM) and x-ray diffraction (XRD). Inductive coupled plasma optical emission spectroscopy was done to detect the impurity concentrations of Iron (Fe) which was found to be present in ppm levels. The nano-particles were found to be nearly spherical in shape in both undoped and doped samples. The particle sizes in undoped samples were found to be increasing with increase in annealing temperatures. As all the copper doped samples were annealed at same temperatures, they were all in the 5 nm size range. The particle size values from XRD and TEM were comparable. Lattice constant and the strain in undoped CeO2 nanoparticles was found to decrease with increase in particle size. In Cu-doped CeO2, lattice constant was increasing with increase in doping concentration levels.;Magnetic properties of these nanoparticles were measured using a superconducting quantum interface device (SQUID) magnetometer. Susceptibility and hysteresis loops plots were plotted using magnetization data from SQUID. Increasing paramagnetism was found with decreasing particle size in the undoped samples which is attributed to increase in Ce3+ concentration. The small amount of ferromagnetism found in the undoped samples is suggested to originate from the Fe present in ppm levels. In Cu-doped CeO2 nanoparticles, the paramagnetic and ferromagnetic parts were found to be increasing with increase in doping concentration of Cu in CeO2. The observed room temperature ferromagnetism in Cu-doped CeO2 is suggested to result from the effects of copper doping