This book comprises a set of lecture notes on rational mechanics, for part of the graduate physics curriculum, delivered by the late Prof. Shirley L. Quimby during his tenure at Columbia University, New York. The notes contain proofs of basic theorems, derivations of formulae and amplification of observations, as well as the presentation and solution of illustrative problems. Collateral readings from more than 50 source references are indicated at appropriate places in the text.