This systematic presentation of the current status and problems of the theory and observations of gravitational lensing starts from the equations of classical electrodynamics and general relativity, and develops for the first time gravitational lens theory from first principles. Beginning with simple models and basic properties of the lens mapping, the book proceeds to more complicated recent analytical and numerical treatments, thereby highlighting the prominent role played by lensing statistics in the interpretation of high-redshift objects. A detailed description of microlensing is given. The potential role of gravitational lenses as astronomical tools, for example, in determining the masses of cosmic objects and the scale of the universe and as natural telescopes, is pointed out. On the observational side, details of several known multiple QSOs, radio rings and luminous arcs, and the difficulties of observation and verification of lens systems are summarized. The basics of catastrophe theory, to the extent that it concerns singularities of plane maps, are derived and some techniques for numerical treatment of gravitational lensing are listed. This book can be viewed both as a textbook and as a research monograph.
