Editors Luis <’A>lvarez-C<’o>nsul, Jos<’e> Ignacio Burgos-Gil, and Kurusch Ebrahimi-Fard present students, academics, researchers, and mathematics professionals working in a wide variety of contexts with a collection of academic papers selected from materials presented at the international research workshop Periods and Motives – A Modern Perspective on Renormalization, held in July of 2012 at the Instituto de Ciencias Matem<’a>ticas in Spain. The contributions that make up the main body of the text are devoted to multiple polylogarithms and linearly reducible Feynman graphs, Dyson-Scwinger equations in the theory of computation, equations D3 and spectral elliptic curves, and a wide variety of other related subjects. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)