Book excerpt: The theory of viscoelasticity has been built up as a mechanical framework for modeling important aspects of the delayed behavior of a wide range of materials. This book, primarily intended for civil and mechanical engineering students, is devoted specifically to linear viscoelastic behavior within the small perturbation framework. The fundamental concepts of viscoelastic behavior are first presented from the phenomenological viewpoint of the basic creep and relaxation tests within the simple one-dimensional framework. The linearity and non-ageing hypotheses are introduced successively, with the corresponding expressions of the constitutive law in the form of Boltzmann’s integral operators and Riemann’s convolution products respectively. Applications to simple quasi-static processes underline the dramatic and potentially catastrophic consequences of not taking viscoelastic delayed behavior properly into account at the design stage. Within the three-dimensional continuum framework, the linear viscoelastic constitutive equation is written using compact mathematical notations and takes material symmetries into account. The general analysis of quasi-static linear viscoelastic processes enhances similarities with, and differences from, their elastic counterparts. Simple typical case studies illustrate the importance of an in-depth physical understanding of the problem at hand prior to its mathematical analysis.