The physics of strongly correlated electron systems is remarkably rich and complex with the interactions between electrons giving rise to a diverse range of physical phenomena including ferromagnetism, metal-insulator transition and superconductivity. Observation of quantum oscillations in the presence of a strong magnetic field is a signature of Fermi liquid behaviour and can be used in conjunction with complementary experimental techniques to map the Fermi surface of a metal. For metallic states, the Fermi surface plays a central role in the understanding of correlated electron systems.

In this dissertation, the author reports his work on the high magnetic field study of three families of strongly correlated electron systems at low temperatures. These include contactless resistivity measurements under pulsed magnetic fields on materials belonging to two families of high temperature superconductors - iron arsenides and underdoped cuprates - as well as high field torque magnetometry and magnetisation measurements on the Kondo insulator samarium hexaboride. Shubnikov-de Haas oscillations observed in the former further our understanding of the nature of the normal states of these high temperature superconductors, crucial to unravel the origin of unconventional superconductivity in these materials. Quantum oscillations observed in samarium hexaboride, on the other hand, points to a paradoxical coexistence of a three-dimensional Fermi surface in the otherwise bulk insulating state of the rare earth hexaboride. The discovery of a possible new phase in matter hints at the work of new physics and an understanding of it is likely to open new exciting areas of research in strongly correlated materials.