Proposal for the experimental study of novel condensed matter systems where the characteristic energy scale of interest is usually (although not exclusively) below 1K. Materials in which high magnetic fields play an important role in either modifying the dimensionality, or the nature of the ground state, or in determining intrinsic physical parameters, are of main interest. Examples of materials which share one or more of these features are organic conductors, heavy electron metals, single and multiple quantum wells and heterostructures, oxide based superconductors, and metal-insulator systems. Current interest is focused on studies of the high magnetic field induced phase transitions in (TMTSF)2ClO4, the magnetic field dependent phase diagram and effective mass of heavy electron materials, the Hall effect and critical currents of High Tc epitaxial thin films, and the bulk magnetization of both semimagnetic semiconductors and copper oxide antiferromagnets. The proposed work will advance present systematic studies on paradigm organic and heavy electron materials, and initiate new studies on recently developed materials such as the higher transition temperature organic salts and copper oxide materials. The proposed work will also include the addition of optical, structural, and tunneling probes to achieve a more microscopic understanding of the phenomena under investigation.