We consider in-depth mechanical, geometric, analytic models of assessment the reliability of systems based on the use of the scheme of cases, Euler-Venn diagrams, generating functions, state diagrams. The methods of qualitative and quantitative assessment of the reliability on the established time interval, based on structural reliability, the importance of a structural element, the sensitivity of the reliability of the system taking into account the duplication of most significant and unreliable elements. Common approaches are illustrated by solving problems of the analysis and synthesis of reliable systems. This book is recommended for engineers, teachers and students of high educational institutions, who in their practice pose and solve problems of reliability of technical systems. The book contains a number of new materials developed by the authors in the last years that have not been published before.