Scanning SQUID Microscope for Studying Vortex Matter in Type II Superconductors Common methods of local magnetic imaging display either a high spatial resolution and relatively poor field sensitivity (MFM Lorentz microscopy) or a relatively high field sensitivity but limited spatial resolution (scanning SQUID microscopy). Since the magnetic field of a nanoparticle or nanostructure decays rapidly with distance from the structure the achievable spatial resolution is ultimately limited by the probe sample separation. This thesis presents a novel method for fabricating the smallest superconducting quantum interference device (SQUID) that resides on the apex of a very sharp tip. The nanoSQUID on tip displays a characteristic size down to 100 nm and a field sensitivity of 10^ 3 Gauss Hz^(1 2). A scanning SQUID microsope was constructed by gluing the nanoSQUID on tip to a quartz tuning fork. This enabled the nanoSQUID to be scanned within nanometers of the sample surface providing simultaneous images of sample topography and the magnetic field distribution. This microscope represents a significant improvement over the existing scanning SQUID techniques and is expected to be able to image the spin of a single electron.