Combining the fundamental principles of flexible body mechanics with engineering applications, this comprehensive work systematically presents the calculation methods for dimensioning load-bearing elements, particularly in the fields of structural and mechanical engineering. Consisting of ten chapters, the first half of the book is dedicated to the core subjects of elasticity, while the second half focuses on applied topics; mathematical information has been added to the introduction of both section groups to facilitate the understanding of the subjects. Appealing to a wide readership at the undergraduate, master's, and doctoral levels, the work is supported by numerous examples, figures, and solved problems. One of the distinguishing features of the book is that it addresses mechanical vibrations and wave equations in a separate chapter, thereby laying the groundwork for earthquake engineering calculations. The dimensioning of rods, thin plates, and thin shells, as well as the stability analysis of flexible structural elements, are also examined in detail. Due to the breadth of its scope, the work is divided into two volumes, bringing together the Fundamental Topics in Volume 1 and the Applied Topics in Volume 2.