A follow-up to the experimental and instrumental aspects described in Basic Principles of Analytical Ultracentrifugation, the volume Sedimentation Velocity Analytical Ultracentrifugation: Discrete Species and Size-Distributions of Macromolecules and Particles describes the theory and practice of data analysis. Mathematical models for the sedimentation process and the evolution of detected signals are developed in a comprehensive framework, jointly with the description of current and historical strategies for how to extract from noisy experimental data the physical parameters of interest, such as size, mass, and shape, composition, and polydispersity of sedimenting particles. The methods are extensively illustrated, and supported with practical applications, as well as cross-references where to find the methods in the public domain software SEDFIT and SEDPHAT. The systems covered are discrete or polydisperse mixtures of sedimenting molecules or particles in dilute solution, such as proteins and other biomolecules and their stable complexes, man-made polymers, and nanoparticles, observed in different optical systems. These methods form the essential foundation for the analysis of dynamic interacting systems, which are covered in a separate volume.