The main emphasis of these Lecture Notes is on constructing solutions to specific viscoelastic boundary value problems; however properties of the equations of viscoelasticity that provide the theoretical underpinnings for constructing such solutions are also covered. Particular attention is paid to the solution of crack and contact problems. This work is of interest in the context of polymer fracture, modelling of material behaviour, rebound testing of polymers and the phenomenon of hysteretic friction.