We describe in this book stable, sub-stable and the most general class of weakly stable distributions and processes, which seem to be good candidates for use in stochastic modeling in many areas. In the firs chapter we recall basic properties of characteristic functions for random variables and vectors. By norm-dependent characteristic functions we describe norm-dependent positive definite matrices, which are extensively used in stochastic modeling random vectors with fixed correlation structure. The second chapter contains five definitions of stable variables together with proofs of their...