Links A link is a union of non-intersecting knots. The Reidemeister moves and colourability apply to links.
Some links have interesting aesthetic and mathematical properties.
Braids A braid is a collection of interwoven strands which are not closed. Graphics Knots also have a certain visual appeal. I've built Borromean rings quite easily, but I can't seem to build the 5-component Brunnian link properly. I follow the picture above, but I can't seem to get something with the right properties. The left and right trefoils are distinct knots, but the figure-8 knot and its mirror image are the same.