This book provides a new Unified Strength Theory and describes its applications. The Unified Strength Theory is a system of yield and failure criteria of materials under complex stresses. It covers the entire range of convex failure criteria, from lower bound (Tresca yield criteria and Mohr-Coulomb failure criteria) to upper bound (twin-shear failure criteria). It also includes the non-convex yield and non-convex failure criteria. A series of new failure criteria and previous failure and yield criteria can be deduced from the Unified Strength Theory. The work presented in this book is unprecedented in the field of strength theory. It is useful for students in understanding the strength theory, for engineers to correctly use it and for researchers to choose an appropriate failure criteria in studying the strenth of materials and structures. An experimental verification, engineering applications, a detailed historical review and more than 1000 references are provided.