The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Adaptive systems are widely encountered in many applications ranging through adaptive filtering and more generally adaptive signal processing, systems identification and adaptive control, to pattern recognition and machine intelligence: adaptation is now recognised as keystone of "intelligence" within computerised systems. These diverse areas echo the classes of models which conveniently describe each corresponding system. Thus although there can hardly be a "general theory of adaptive systems" encompassing both the modelling task and the design of the adaptation procedure, nevertheless, these diverse issues have a major common component: namely the use of adaptive algorithms, also known as stochastic approximations in the mathematical statistics literature, that is to say the adaptation procedure (once all modelling problems have been resolved). The juxtaposition of these two expressions in the title reflects the ambition of the authors to produce a reference work, both for engineers who use these adaptive algorithms and for probabilists or statisticians who would like to study stochastic approximations in terms of problems arising from real applications. Hence the book is organised in two parts, the first one user-oriented, and the second providing the mathematical foundations to support the practice described in the first part. The book covers the topcis of convergence, convergence rate, permanent adaptation and tracking, change detection, and is illustrated by various realistic applications originating from these areas of applications.