The book is devoted to mathematical foundations providing synthesis and analysis of control and adaptation algorithms targeting modern telecommunication systems (TCS). These algorithms are finding more and more applications in modern telecommunication technologies and they determine the efficiency of TCS. The concept of telecommunication management network is used as a base methodology. The most popular technologies and network management methods are discussed. They include such issues as Common Management Information Protocol, Remote Network Management Protocol Information Base, Simple Network Management Protocol, and Net Flow. The methods of state variables are used as the main mathematic approaches for simulating control tasks. It allows solving the dynamic problems in the recursive style. The decomposition theorem is used for synthesis of control algorithms. Such issues as control algorithms for system observation and system state are discussed in details. The interpretation of applicability for discussed algorithms is given. Some part of the book is devoted to methods of statistic gathering and suppressing of a priori uncertainty. They are reduced to constructing adaptive procedures and algorithms of self-organization and self-repairing for intellectual taught systems. The neural networks, multifunctional automata and Petri nets are discussed as examples. Also, tasks and problems of business processes management are shown in their connection with TCS. Our book targets on students, PhD students and professionals in the area of telecommunications. We hope it will be useful for everybody connected with the new information technologies.