The research objective of this project is to untangle the influence of topology on the mechanics of complex knots, particularly those used in surgical procedures, by tying together experiments, computation, and theory. Given that the nonlinear geometry of physical knots tied on filaments with frictional interactions at self-contacts cannot be accessed through 2D imaging, 3D volumetric imaging will be performed, using a state-of-the-art, high-performance X-ray micro-CT system. First, we will study the nonlinear geometry of elastic knots, in particular, the overhand and figure-of-eight-knots, both in loose and in tight configurations. Precision 3D experimental data will be used to validate an existing computational framework based on the Discrete Elastic Rod method, which will be specialized for elastic knots. Secondly, we will focus on the mechanics of surgical knots. The geometries of a subset of standard surgically-relevant knots will be thoroughly quantified and evaluated using the data from the micro-CT scanner. The goal is to model the mechanics of these knots and to categorize their mechanical performance. Then, the geometry and response of continuous running sutures will be investigated by analyzing the contact tractions that the knot system exerts on the underlying soft tissue. The proposed research will be the first time that predictive models, informed by precision experiments, will quantify the dependence of the mechanical response of surgical knots as a function of their topology, friction at the self-contacting regions, and the mechanical properties of the suturing thread. A fundamental understanding of knots and the development of accurate analytical and computational tools will open the door for an evaluation of autonomous robotic sutures and could have a long-term impact on minimally invasive and robot-assisted surgery.