Nonlinear polymer topologies composed of cyclic and branched polymer segments are systematically classified by reference to constitutional isomerism in a series of alkanes (CnH2n+2), monocycloalkanes (CnH2n), and polycycloalkanes (CnH2n-2, CnH2n-4 etc). Thus. the total number of chain ends (termini) and of branch points (junctions) are maintained as invariant parameters, as well as the number of branches at each junction and the connectivity of junction. On the other hand. the distance between two adjacent junctions and that between the junction and terminus are taken as variant parameters. On the basis of the classification of polymer topologies, a novel synthetic strategy by an "electrostatic self-assembly and covalent fixation" technique has been proposed to construct a variety of topologically unique polymer architectures.