This book provides an accessible introduction to the mathematical methods of
quantum optics. Starting from first principles, it reveals how a given system of atoms
and a field is mathematically modelled. The method of eigenfunction expansion and the
Lie algebraic method for solving equations are outlined. Analytically exactly solvable
classes of equations are identified. The text also discusses consequences of Lie
algebraic properties of Hamiltonians, such as the classification of their states as
coherent, classical or non-classical based on the generalized uncertainty relation and the
concept of quasiprobability distributions. A unified approach is developed for
determining the dynamics of two-level and a three- level atom in combinations of
quantized fields under certain conditions. Simple methods for solving a variety of linear
and nonlinear dissipative master equations are given.