This paper addresses one of the fundamental tasks for the aerial assembly of tensile structures: aerial knot-tying. It presents a framework for representing and realizing knots with flying machines. A suitable representation of the knot topology is introduced taking into account the use of supporting elements and the characteristics of flying machines. This information is then translated into three-dimensional trajectories for the vehicle performing the aerial knot-tying task. Furthermore, preliminary results suggest that the quality of the resulting knot can be improved by the use of an iterative learning algorithm. Experiments are performed with quadrocopters to validate the proposed approach. An accompanying video shows the aerial knot-tying process.