This is an up-to-date introduction to the theory of impulsive control in nonlinear systems - a branch of optimal control theory, which is tightly connected to the theory of hybrid systems. The text introduces the reader to the area of optimal control problems with discontinuous solutions, discussing the application of a new and effective method of discontinuous time-transformation. With a large number of examples, illustrations, and applied problems arising in the area of observation control, this book should be useful as a textbook or reference for a senior or graduate-level course on the subject, as well as a reference for researchers in related fields.