This manual is devoted to the classical and quantum phases in wave and particle optics from the viewpoint of both theory and applications. Wave and beam light optics are reviewed in detail, sequencing optical imaging and holography in linear optics and phase conjugation methods in nonlinear optics. Photon optics is embodied as quantum optics with modes treated as quantum harmonic oscillators. The importance of the Wigner function for the phase space description in the context of canonical quantization is respected and the method of quasidistributions related to operator orderings in the second-quantized theory is exposed. The history of the quantum phase problem is included and brought up-to-date, characterized by renewed interest in the solution to the problem. Approaches based on exponential phase operators, discrete phase states, the enlargement of the Hilbert space of the harmonic oscillator leading to the phase representations and distributions, together with solutions motivated by the quasidistributions, are introduced. The operational approach to the quantum phase is contrasted with the previous formalisms. In addition to the study of the coherent states and the ordinary squeezed states from the viewpoint of the quantum phase, the quantum statistics of phase-motivated special states of the light field are analyzed.
