The purpose of this project is to provide basic knowledge about how the properties of superconductors vary at the local level under strong magnetic fields. New phases such as the FFLO state in Pauli limited superconductors or fully polarized vortex phase in ferromagnetic heavy fermions have been predicted. However, no direct observation of such phases using real space imaging has been reported yet. The goals of the project are to investigate unconventional high magnetic field superconducting phases and to understand their relationship with the normal state electronic structure. In particular, we will directly image the spatial variations in the superconducting pair function and determine the electronic structure through Landau level spectroscopic measurements. The latter is a new local technique which we will first implement here. To achieve these objectives, dilution refrigerator Scanning Tunneling Microscopy (STM) studies will be performed down to the mK regime and under magnetic fields up to 17 T. Within the project, a compact STM device will be built to operate at the highest available magnetic fields and enable the possibility of future STM measurements in international high field facilities. The microscopic approach to high field superconductivity proposed here will bring about new challenges and opportunities through the combination of local studies and novel superconducting properties.