Accuracy is one of the fundamental characteristics and one of the most important indexes of the quality of machines and robots. It significantly defines their structure and applications and, in turn, depends on their structure and applications. Accuracy provision, maintenance, and enhancement are permanently hot problems in modern manufacturing and manufacturing science. The book is being published in two volumes and comprises the Introduction and four parts including 18 chapters with consecutive numbering, and three appendices. Each part combines a theoretical chapter with applications to machines and robots with different kinematic types. The formalized consideration is accompanied with application examples, which, as a rule, are explained with numerical solutions using realistic initial values. Volume 1 includes Introduction, Parts I and II (Chapters 1-12), and hence, embraces the general accuracy definitions, nominal machine functioning models, and geometrical accuracy problems. Volume 2 includes Parts III and IV and is available separately. The book is intended for machine and robot designers and researchers, university graduate and senior undergraduate students, and may be also useful for instructors in the mechanical engineering field for teaching processes.