This thesis presents an exploration of topological interlocking system of structural assemblies. By analysing existing topological structures, a mathematical theory is constructed to design different topological interlocking systems based on various existing design techniques. A structural equilibrium analysis method is presented for the designed structural assemblies through a detailed analysis of the collapse mechanism. The method also features a novel way to transform indeterminate problems into determinate problems using the geometric relations, by an implementation of the half-edge data structure in mesh manifold computation. The thesis also briefly introduces a mapping strategy based on conformal mapping on NURBS surface to design freeform topological structural assemblies.