Ph.D. (Physics) / Compounds of rare-earth (RE) elements (Ce, Yb, Eu) as well as actinide element U with partially filled 4f or 5f shells have been receiving considerable attention in the field of low temperature studies. This stems from the diversity of magnetic ground state exhibited by the compounds. These range from non-magnetic, metallic, ferromagnetic or antiferromagnetic ordered state. The nature of the ground state depends on the balance between the on-site Kondo interaction, which mostly favours a local non-magnetic singlet and also the indirect Rudderman-Kittel-Kasuya- Yosida (RKKY) exchange interactions. The interactions of the localized f moments with their environment result in the crystal electric field (CEF) effects at the rare-earth (RE) ion site which splits the free-ion ground-state multiplet. The competing energy scales of CEF splitting, Kondo and RKKY interaction cause the large variety of exceptional phenomena observed in rare earth systems, such as heavy-fermion (HF) behaviour, intermediate valence, unconventional superconductivity, and quantum criticality. Generally, the low-temperature properties of RE systems depend sensitively on the position of the undisturbed 4f state with respect to the Fermi level. Thus, the hybridization between the 4f and conduction-electron states may give rise to either an enhanced density of states (DOS) near the Fermi level in HF metals or to the formation of a gap at Fermi level in Kondo insulators. Recent considerable research interest in strongly correlated electron systems (SCES) studies has been the study of intermetallic compounds close to magnetic instability and the introduction of non-Fermi-liquid (NFL) state. NFL behaviour in f-electron systems is characterized by special power laws and logarithmic divergences in temperature of the physical properties of materials at low temperatures...