Semiconductor quantum rings are of great fundamental interest because their non-trivial topology creates novel physical properties. At the same time, toroidal topology is difficult to achieve for colloidal nanocrystals and epitaxially grown semiconductor nano structures. In this work, we introduce the synthesis of luminescent colloidal CdSe nanorings and nanostructures with double and triple toroidal topology. The nanorings form during controlled etching and rearrangement of two-dimensional nanoplatelets. We discuss a possible mechanism of the transformation of nanoplatelets into nanorings and potential utility of colloidal nanorings for magneto optical (e.g., Aharonov-Bohm effect) and other applications.