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This volume presents recent developments in the area of Levy-type processes and more general stochastic processes that behave locally like a Levy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Levy-type process: a non-random function which is a counterpart of the characteristic exponent of a Levy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed,...