The central theme of this book is the application of the linear filtering theory to the vibration of structures in a fluid. Emphasis is placed on the mathematical models which, in the theory of systems, characterize the state of a dynamic system. The mathematical models are in the form of linear Ito stochastic differential equations. Discretization of the models, which leads to straightforward computer applications, is also discussed. The book also presents an approach to nonlinear problems based on the expansion of random functions in a series. To elucidate the proposed approach, examples on the application of Kalman filters, which refer to the vibrations of cylinders in waves, are cited. This provides a practical orientation to complement the proposed theory and contributes to a clearer and deeper understanding of the subject matter.