This book presents an introduction to viscoelasticity; in particular, to the the- ories of dilute polymer solutions and melts, and dilute suspensions of rigid particles in viscous and incompressible fluids. These theories are important, not just because they apply to practical problems of industrial interest, but because they form a solid theoretical base upon which mathematical tech- niques can be built, from which more complex theories can be constructed, to better mimic material behaviour. The emphasis is not on the voluminous cur- rent topical research, but on the necessary tools to understand viscoelasticity at a first year graduate level. 1 Viscoelasticity, or Continuum Mechanics, or Rheology (certainly not to be confused with Theology) is the science of deformation and flow. This def- 2 3 inition of was due to Bingham, who, together with Scott-Blair and Reiner, helped form The Society of Rheology in 1929. Rheology has a distinguished history involving high-profile scientists. The idea that everything has a time scale, and that if we are prepared to wait long enough then everything will flow was known to the Greek philosopher Heraclitus, and prior to him, to the 4 Prophetess Deborah – The Mountains Flowed Before The Lord. Not surpris- ingly, the motto of the Society of Rheology is 1ravra pet (everything flows), a saying attributed to Heraclitus.