The high degree of modification through chemical substitution afforded by the perovskite crystal structure and its related counterparts allows a systematic study of structure-property relationships critical to understand the wide variety of exotic phenomena observed in these materials where the spin, charge, orbital, and lattice degrees of freedom are highly correlated. From the multiple phenomena observed in these materials, which includes multiferroicity, catalytic activity, and high temperature superconductivity, this study is concerned with a material that displays colossal magnetoresistance (CMR), La₂₋₂xSr₁₊₂xMn₂O₇; this is a naturally bilayered manganite that exhibits CMR at a paramagnetic to ferromagnetic transition that coincides with an insulator to metal transition. The strong correlation between different degrees of freedom in the material leads to considerable variation in its magnetic properties due to doping even in the small range studied of 0.32 [less than or equal to] x [less than or equal to] 0.4, where the easy axis of magnetization changes from the c-axis to the ab plane. Magnetic force microscopy (MFM) was used for this part of the work, to visualize the local variation of the out of plane (c-axis) magnetization or magnetic microstructure of La₂₋₂xSr₁₊₂xMn₂O₇ for 0.32 [less than or equal to] x [less than or equal to] 0.4 at the exposed ab surface and its evolution due to an applied magnetic field at 4 K. For the x = 0.32 composition, which is close to the out of plane to in plane magnetization transition, a strong preferred magnetization direction within the ab plane or magnetocrystalline anisotropy was observed. The stray magnetic field of the MFM tip perturbs the magnetic microstructure of low coercivity materials like diluted magnetic semiconductors, making it unsuitable for the study of such materials. For this reason, as part of this project a scanning Hall probe microscope (SHPM), a magnetic imaging technique complementary to MFM that uses a Hall sensor that provides a magnetically non-invasive calibrated measurement of the stray fields at the surface of a sample with good resolution (~ 1 [micrometer]), was designed. The construction of a compact cryogenic variable-temperature (77 - 300 K) SHPM, highlighting its features, is described. / text