The objective of this project is to explore novel phenomena of heavy fermion systems. The focus will be on low temperature novel properties such as quantum criticality, unconventional superconductivity and multipole ordering, which will leads to new horizon not only of heavy fermion physics, but also of material science. We will concentrate on: (1) new materials and high quality single crystals, (2) precise temperature-pressure-field (T,P,H) phase diagrams, (3) quantum singularities and Fermiology, (4) the mechanism of unconventional superconductivity including ferromagnetic superconductor, (5) field-induced phenomena.To reach our targets, we will first attempt to grow many new compounds based on U, Ce, Yb and other rare earth elements with a careful choice of target, using various techniques. Very high quality single crystals can be a breakthrough in this field of research, in particular for unconventional superconductivity. Then, we will measure their low temperature properties with various experimental techniques under extreme conditions, namely low temperature, high field, high pressure. Activities of material growth and studies of their properties will be coordinated in order to provide rapid a feedback. This work will be comforted by theoretical work. To carry out specific experiments, we will develop a new AC calorimetry system under extreme conditions and a de Haas-van Alphen (dHvA) measurement system. With this experimental method, we aim to directly observe the heavy electronic state. This is a major issue to clarify the possible Fermi surface instability at quantum singularities. The high quality samples will be supplied to other groups in order to extend our macroscopic and microscopic experimental multi approach.