Vortex waves have become a major preoccupation of workers in superfluidity. This book discusses the properties of quantized vortex lines in superfluid helium II in the light of research on vortices in modern fluid mechanics. The author begins with a review of classical fluid dynamics relevant to the main topics of the book. This is followed by a presentation of basic material on helium II and quantized vortices. The following chapters deal with various different aspects of the subject including vortex dynamics and mutual friction, the structure of quantized vortices, vortex arrays, and vortex waves. The book concludes with an introduction to two currently active topics, namely superfluid turbulence and the nucleation of quantized vortices.