In nature, different materials undergo phase transition and change phases which is typically controlled by temperature. From boiling of water to more complex phenomena such as superconductivity, Bose-Einstein condensation there exist a wide variety of examples of phase transition. Unlike these thermal phase transitions, several materials and systems undergo phase transitions driven solely by quantum fluctuations. This kind of phase transition is known as quantum phase transition (QPT), which is strictly defined as a phase transition occurring at absolute zero. Nature of such quantum fluctuations are quite distinct from those of thermal fluctuations, and more advanced techniques are required to understand the physical properties of the systems near such a quantum critical point. Quantum field theoretic methods, quantum Monte-Carlo techniques, exact diagonalization, diff erent types of variational methods can be used to understand various phases and QPT of correlated systems. Recent experimental demonstration of super-fluid (SF) to Mott insulator (MI) transition in trapped bosonic atoms in an optical lattice, has opened up a new direction to study various exotic phases and quantum criticality of ultracold atomic gases (both fermionic and bosonic) in optical crystals. Dipolar condensate of 52Cr atoms with long range anisotropic interactions shows the possibility of observing novel phases such as supersolids, charge density waves etc. Typical class of problems that are studied within this part of activity are, General analysis of Quantum Criticality, Exotic phases and Quantum criticality in correlated bosons and fermions in optical lattice, Ultracold quantum gases in a trap.