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This textbook charts out an easy-to-comprehend account of the methods of random vibrations, aided by modern yet basic concepts in probability theory and random processes. It starts with a quick review of certain elements of structural dynamics, thus setting the stage for their seamless continuation in developing techniques for response analyses of structures under random environmental loads, such as winds and earthquakes. The book also offers a few glimpses of the powerful tools of stochastic processes to kindle the spirit of scientific inquiry. By way of applications, it contains numerous illustrative examples and exercises, many of which relate to practical design problems of interest to the industry. A companion website provides solutions to all the problems in the exercises. For the benefit of the prospective instructors, a semester-long schedule for offering a course on Random Vibrations is also suggested.