The book "Mechanics of Periodically Heterogeneous Structures" offers a comprehensive and rigorous presentation of mathematical homogenization theory. It aims to fill a gap in the analytical and numerical analysis of the asymptotic behaviors of heterogeneous systems. The authors, L.I. Manevitch, I.V. Andrianov, and V.G. Oshmyan, illuminate both static and dynamic aspects and provide numerous concrete applications related to composite materials as well as heterogeneous plates and shells. The work includes detailed numerical results, solutions for cell problems, calculations of high-order terms in asymptotic expansions, and analyses of boundary layers. This comprehensive treatment makes the book a valuable resource for professionals and students engaged in the mechanics of heterogeneous materials.