This book deals with some inverse problems of mathematical physics. The choice of material was determined by the author's interest in the latest developments in this field. The results presented have been published in different mathematical journals, but have been partly revised before inclusion in this volume. The book does not aim to give a systematic presentation of the theory of inverse problems but introduces some new methods for studying inverse problems and gives obtained results, which are related to the conditional well posedness of the problems. The main focus lies on time-domain inverse problems for hyperbolic equations. The final chapter deals with the kinetic transport equation.