Matrix Analysis -- Vibrations of Discrete Systems -- Jacobi Matrices -- Inverse Problems for Jacobi Systems -- Inverse Problems for Some More General Systems -- Positivity -- Isospectral Systems -- The Discrete Vibrating Beam -- Discrete Modes and Nodes -- Green’s Functions and Integral Equations -- Inversion of Continuous Second-Order Systems -- A Miscellany of Inverse Problems -- The Euler-Bernoulli Beam -- Continuous Modes and Nodes -- Damage Identification.In the first, 1986, edition of this book, inverse problems in vibration were interpreted strictly: problems concerning the reconstruction of a unique, undamped vibrating system, of a specified type, from specified vibratory behaviour, particularly specified natural frequencies and/or natural mode shapes. In this new edition the scope of the book has been widened to include topics such as isospectral systems- families of systems which all exhibit some specified behaviour; applications of the concept of Toda flow; new, non-classical approaches to inverse Sturm-Liouville problems; qualitative properties of the modes of some finite element models; damage identification. With its emphasis on analysis, on qualitative results, rather than on computation, the book will appeal to researchers in vibration theory, matrix analysis, differential and integral equations, matrix analysis, non-destructive testing, modal analysis, vibration isolation, etc. "This book is a necessary addition to the library of engineers and mathematicians working in vibration theory." Mathematical Reviews.