This book presents the theory of free, forced and transient vibrations of single degree, two degree and multi-degree of freedom, undamped and damped, lumped parameter systems and its applications. Free and forced vibrations of undamped continuous systems are also covered. Numerical methods like Holzer's and Myklestad's are also presented in transfer matrix form. The emphasis is on modelling of engineering systems. Examples chosen, even though quite simple, always refer to practical systems. Experimental techniques in vibration analysis are discussed at length in a separate chapter and several classical case studies are presented.