Fractional Calculus and Waves in Linear Viscoelasticity (Second Revised Edition) is a self-contained treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation and waves) with particular regard to models based on fractional calculus. It serves as a general introduction to the above-mentioned areas of mathematical modelling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature. In particular the relevant role played by some special functions is pointed out along with their visualization through plots. Graphics are extensively used in the book and a large general bibliography is included at the end.This new edition has been entirely revised and updated to reflect recent developments in the field. This Second Revised Edition keeps the structure of the First Edition but all chapters and appendices have been revised and expanded.