Constitutive modelling (or mechanics) is the most intensive research field within solid mechanics. This work combines constitutive modelling and the corresponding numerical solution strategies. It is geared towards a presentation of various important concepts, and contains specific models that are discussed as it covers this broad topic. For every area considered, the exposition is self-contained and provided with extensive references for further reading. The book is divided into two complementary volumes - Part1- Classical Topics, and Part 2- Numerical and Thermodynamical Topics. This is an excellent reference providing a broad treatment of the state-of-the art for all levels. It will be an essential desk reference for post-docs, as well as researchers at all levels, not only in solid mechanics, but also computational mechanics and materials science.