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The book is intended to construct a mathematical theory of modeling the asynchronous circuits from the digital electrical engineering. It uses the general concept of system providing models for the functional blocks, where modeling is present at a synthetical level as well as the particular concept of delay (stable system with 1-dimensional input and 1-dimensional output), providing models for the gates and wires, where modeling is present at an analytical level. The concept of asynchronous system is defined in the sense that can be referred to in literature as 'the input-output behavior of a non-initialized, non-deterministic system', i.e. as a multi-valued function. The mathematical facts we present may also be useful in studying the general topics of the systems theory as well as in establishing connections between this theory and other theories: Petri nets, temporal logic, timed automata, dynamical systems. The first part of the book is dedicated to the general systems theory, the second to delay theory and the third to the Boolean dynamical systems. The book addresses to researchers in systems theory and computer science.