This book explores the crucial role of inverse problems across various fields of applied science and technology. By examining physical phenomena governed by mathematical physics, it addresses the challenge of determining unknown parameters and developing non-destructive methods for systems of solid and structural mechanics. It delves into the inherent mathematical complexities of inverse problems and presents innovative strategies for overcoming these issues. Aimed at doctoral students and researchers in civil and mechanical engineering, mathematical physics, and applied mathematics, the book provides a solid theoretical foundation and equips readers with the necessary mathematical and computational tools to tackle diverse inverse problems.