This is an up-to-date review of studies in the physics of pulsed electrical discharges in a vacuum. It gives the reader detailed information on the processes occurring at electrodes and in vacuum gaps and on the mechanisms of discharge initiation and development. Modern techniques and equipment are described in detail. Their high temporal and spatial resolution may be used to solve a number of problems concerning the short-term and microscopic aspects of discharges. A summary is given of a great deal of experimental data on the kinetics of vacuum breakdown. The authors used these results to identify a series of steps in the vacuum breakdown phenomenon. They were the first to discover and describe the explosive electron emission phenomenon and to show its fundamental role in the spark and the arc stages of a discharge. The information in this book may encourage the reader to design new experiments. The results presented may be applied to solve specific research or engineering problems.