The Poincaré plot, named after Henri Poincaré, is a popular two-dimensional visualization tool for dynamic systems due to its intuitive display of the dynamic properties of a system from a time series. This book presents the basis of the Poincaré plot and focuses especially on traditional and new methods for analyzing the geometry, temporal, and spatial dynamics disclosed by the Poincaré plot to evaluate heart rate variability (HRV). Mathematical descriptors of the Poincaré plot have been developed to quantify autonomic nervous system activity, including sympathetic and parasympathetic modulation of heart rate. Poincaré plot analysis has thus been used in various clinical diagnostic settings such as diabetes, chronic heart failure, chronic renal failure, and sleep apnea syndrome. The primary aims of quantifying the Poincaré plots are to discriminate healthy physiological systems from pathological conditions.