This book is about musical rhythm. More precisely, it is concerned with computer programs that automatically extract rhythmic descriptions from musical audio signals. New algorithms are presented for tempo induction, tatum estimation, time signature determination, swing estimation, swing transformations and classification of ballroom dance music styles. These algorithms directly process digitized recordings of acoustic musical signals. The backbones of these algorithms are rhythm periodicity functions: functions measuring the salience of a rhythmic pulse as a function of the period (or frequency) of the pulse, calculated from selected instantaneous physical attributes (henceforth features) emphasizing rhythmic aspects of sound. This book substantially contributes to the field of computational rhythm description by proposing an unifying functional framework; by reviewing the architecture of many existing systems with respect to individual blocks of this framework; by reporting on the first public evaluation of tempo induction algorithms; and by identifying promising research directions.