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QH323.5.SPR. FCT 94508 Mathematical modeling of complex biological systems QA269.SPR. FCT 94517 Advances in dynamic games QA9.45.SPR. FCT 94520 Function algebras on finite sets QA329.SPR. FCT 94521 Analysis of Toeplitz operators QC175.SPR. FCT 94527 Vortices in Bose QA305.SPR. FCT 94528 Automatic differentiation QD462.SPR. FCT 94529 Méthodes mathématiques en chimie quantique

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Since the late 1980s, Toeplitz operators and matrices have remained a ?eld of extensive research and the development during the last nearly twenty years is impressive. One encounters Toeplitz matrices in plenty of applications on the one hand, and Toeplitz operators con?rmed their role as the basic elementary building blocks of more complicated operators on the other. Several monographs on Toeplitz and Hankel operators were written d- ing the last decade. These include Peller’s grandiose book on Hankel ope- tors and their applications and Nikolski’s beautiful easy reading on operators, functions, and systems, with emphasis on topics connected with the names of Hardy, Hankel, and Toeplitz. They also include books by the authors together withHagen,Roch,Yu.Karlovich,Spitkovsky,Grudsky,andRabinovich.Thus, results, techniques, and developments in the ?eld of Toeplitz operators are now well presented in the monographic literature. Despite these competitive works, we felt that large parts of the ?rst edition of the present monograp- whichismeanwhileoutofstock-havenotlosttheirfascinationandrelevance. Moreover, the ?rst edition has received a warm reception by many colleagues and became a standard reference. This encouraged us to venture on thinking about a second edition, and we are grateful to the Springer Publishing House for showing an interest in this.

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