This book was written by a group of authors and provides a systematic dis- cussion of questions related to bremsstrahlung in many-particle systems. A number of new results have recently been obtained in this area which require a fundamental revision of the previously existing traditional concepts of bremsstrahlung. This ap- plies both to complicated atoms containing a large number of electrons and to the additional bremsstrahlung in a system of many particles forming a medium. In fact, the traditional approach was rigorously applicable only either to isolated "structureless" particles (e. g. , to the emission of an electron on a proton) or to par- ticles radiating in the limit of extremely high frequencies. Polarization effects (either polarization of an atom itself by an incident particle or polarization of the medium surrounding an atomic particle) have a significant effect in the practically important optical and x-ray frequency ranges and sometimes even predominate. The first effect has come to be known as polarization atomic (or dynamic) bremsstrahlung and the second, as polarization transition bremsstrahlung. The au- thors of this book use a single term: polarization bremsstrahlung. It seems that, in contrast to earlier ideas on the subject, bremsstrahlung during collisions of heavy incident particles with atoms is by no means small and is entirely caused by polar- ization effects.