This comprehensive book on Linear Mechanics was designed by the author to fill what he perceived as a gap in the literature of mathematics, which often treated the subject in a manner he described as both sketchy and incomplete. In writing A First Course in Linear Mechanics, the author had the goal in mind of writing the finest book that has ever been written on the subject. Generations of teachers and students have benefited from Nash's thorough presentations and concise results. Suitable for advanced undergraduates and graduate students of mathematics, his treatment examines a wide range of topics giving the reader a breadth of understanding and insight into current mathematical research areas.