First volume of second edition of Rotor Systems book covers the analysis of simple rotors including rotor dynamic phenomena, gyroscopic effects and instabilities with the help of simple rotor-bearing models. It is biased towards the FEM analysis of complex rotors, both for torsional and transverse vibrations including transfer matrix method. Instabilities of the rotor system is covered for simple as well as complex rotor system considering bearings, seals, internal damping, unsymmetrical shaft stiffness and unsymmetrical rotor inertia. Covers rotor analysis from simple single degree of freedom to multi-degree of freedom with lots of solved examples Illustrates bearing and seals theory with perspective to rotor dynamics Discusses finite element method and transfer matrix methods for torsional and transverse vibration analysis Includes elemental equations derived from Euler-Bernoulli beam model, Rayleigh’s beam model and Timoshenko beam model Explores instability in rotor systems considering the hydrodynamic bearing and seal models, internal damping, unsymmetrical shaft stiffness and unsymmetrical rotor inertia This book is aimed at senior undergraduate/graduate students in mechanical engineering, rotordynamics, rotating machinery/turbomachinery, and related fields.