This book considers the phenomena in the framework of a measurement procedure mapping random samples of Markov branching process. The statistical theory of cascade processes can be developed in three ways. The first way is connected with the further development of the classical (forward) kinetic equation system with increasing number of arguments, that is, involving many particle distribution functions along the lines of the standard approach in statistical physics (Bogoliubov, Balescu).The second way to build the theory, choosing for this book, is based on a generalization of the backward (adjoint, in the Lagrange sense) kinetic equations. This approach is borrowed from the theory of nuclear reactors with neutron multiplication (Marchuk, Lewins). The third way is dealing with global nature of the information extracted from individual cascades, such as the direction of the shower axis, position of the center of gravity, the width of the distribution, the shape of the detector pulse, and the image parameters in Cherenkov light images. In contrast to individual particles, these characteristics relate to the cascade as a whole and for this reason, it may be treated as some sort of collective variables (Bohm, Feynman).