RNA can self-assemble into complex structures through base pairing, as well as encode information and bind with proteins to induce enzymatic activity. Furthermore, RNA can possess intrinsic enzymatic-like (ribozymatic) activity, a property that, if necessary, can be activated only upon the binding of a small molecule or another RNA (as is the case in aptazymes). As such, RNA could be of use in nanotechnology as a programmable polymer capable of self-assembling into complex topological structures. In this chapter we describe a method for designing advanced topological structures using self-circulating RNA, exemplified by three tiers of topologically manipulated self-assembling synthetic RNA systems. The first tier of topological manipulation, the RNA knot is a physically locked structure, formed by circularizing one monomer of knotted single-stranded RNA left with loose ends (an "open" knot). The second tier, a two interlocking ring system, is made by interlocking two circular RNA components: a circular RNA target, and an RNA lasso designed to intercalate the target before circularizing. The third tier naturally extends this system into a string of topologically locked circular RNA molecules (an RNA chain). We detail the methodology used for designing such topologically complex RNAs, including computational predictions of secondary structure, and where appropriate, RNA-RNA interactions, illustrated by examples. We then describe the experimental methods used for characterizing such structures, and provide sequences of building blocks that can be used for topological manipulation of RNA.