Even people who do not like spiders can find much to love in the red backed jumping spider. First of all they are cute.(well, cute for a spider). Stocky and fuzzy, with eight eyes positioned across a broad face, they are somehow a little less spidery-creepy than a black widow. If you are impressed by athletic prowess, they are stars in the long jump category — reportedly able to jump 30 to 40 times their body length. A 6-foot man with that ability could jump half a football field with room to spare. Wonder of wonders, this is not directly accomplished with muscles. Spiders of all sorts use hydraulics to extend their legs. A quick Google search under “Spider hydraulics” will turn up dozens of articles about it. That's the reason their legs curl up as they die. They are effectively spring loaded to that position. It is internal pressure that extends them and allows the animal to move about.
Like rock climbers, wherever they go they attach a safety line. If they are dislodged, they can recover immediately.
Some articles I've read point out they can calculate a trajectory around an obstacle, attach a silk drag line, jump, and swing past a barrier to get to their target. All of which is a pretty sophisticated piece of math for something with a brain the size of a bit of lint.
If you just don't like spiders at all, you can take cheer from the fact that they quite effectively hunt other spiders. I'd say about half of the photos I've taken of jumping spiders with prey are spider on spider. It is fascinating to watch them acquire a target, stalk it to comfortable distance and suddenly leap onto it. When it goes right, it is all over very quickly.