  We introduce the transverse Ising model as a prototype for discussing quantum
phase transition. Next we introduce Suzuki-Trotter formalism to show the
correspondence between $d$-dimensional quantum system with a
$(d+1)$-dimensional classical system. We then discuss transverse Ising spin
glass models, namely S-K model, E-A model, and the $\pm J$ model with Ising
spin in transverse field. We briefly discuss the mean field, exact
diagonalization, and quantum Monte Carlo results for their phase diagrams. Next
we discuss the question of replica symmetry restoration in quantum spin glasses
(due to tunnelling possibility through the barriers). Then we discuss the
quantum annealing technique and indicate its relationship with replica symmetry
restoration in quantum spin glasses. We have also breifly discussed the
possibility of Quantum Annealing in context of kinetically constrained systems.
  Mean-field calculation for BCS superconductivity, Real-space RG calculation
for one dimensional transverse Ising system, scattering amplitude calculation
for tunneling through asymmetric barrier (useful for quantum kinetically
constrained system) are given in the appendices.
