Rotor dynamics is both a classical and a modern branch of engineering science. The rotation of rigid bodies, mainly those with regular shapes such as cylinders and shafts, has been well understood for more than a century. However, analyzing the rotational behavior of flexible bodies, especially those with irregular shapes like propellers and blades, requires more modern tools such as finite elements, hence the title and focus of this book. In the dozen years since the original publication, this book was used in teaching engineering students at universities and in consulting in the industry. During those activities, several topics were deemed to require further explanations. Students requested a deeper finite element technology foundation in certain places to make the book self-contained in that regard also. Some desired more details about the computational and numerical solutions. These requests are answered in new sections of this edition. Practicing engineers asked for a detailed industrial application case study and such was added in a new chapter dealing with wind turbines. This book is composed of two parts, the first focusing on the theoretical foundation of rotor dynamics and the second focusing on the engineering analysis of industrial structures. The theoretical foundation is built on physics, calculus, and finite element technology chapters. Computational and numerical techniques provide free vibration and response analyses solutions. The industrial engineering analysis part contains chapters analyzing jet-engine turbine wheels, aircraft propellers, and wind turbine blades. This book concludes with a new industrial case study based on a recent modern wind turbine development project.