The book describes the methodologies for dynamics formulation, balancing, and optimizing dynamic quantities of multibody systems, such as mechanisms and robots. The writing equations of motion of multibody systems are simplified by using Decoupled Natural Orthogonal Complementary (DeNOC) matrices-based methodology originally proposed by the second author. Writing equations of motion using a DeNOC based approach enables the analytical expressions of even complicated systems which provide better physical insights of the system at-hand. The DeNOC based dynamics formulation of multibody systems is extended from system of continuum rigid-link to discrete equivalent system of point-masses coined as DeNOC-P. The dynamics formulation representing a link as point-masses is exploited to minimize the dynamic quantities shaking forces, shaking moments, or driving torques/forces by optimizing the mass redistribution of the link. Several numerical examples, such as carpet scraping machine, PUMA robot, Stewart platform, etc., are illustrated. The book also demonstrates a shape optimization methodology to realize the link with optimized mass redistribution. This textbook can be prescribed for teaching a course on dynamics and balancing of multibody systems at undergraduate and postgraduate level.