Starting with the analysis of simple discrete systems, the essential ideas of building up the governing equations of the system from those of its constituent parts is illustrated. The techniques of deriving a discrete set of equations for continuous systems are then outlined; specifically the variational and weighed residual procedures are examined and illustrated through some simple examples. The course then concentrates on applications to structural mechanics of solids. Programming for finite elements is also covered and students are encouraged to design and develop FEM software.