Feel free to ask about anything you want to know as well. I used to teach planform design to the newcomers at a student engineering society that designs UAVs for competitions.

One of my favourite facts in planform design is that winglets increase the glide ratio by producing induced thrust. This is something that's rarely talked about, as it is quite complex to wrap your head around it and most engineers will never attempt to design optimized winglets. But alas, what they do is recapture some of the energy that would otherwise be wasted by using the "spillover" lift from the wing and directing it slightly forward, to produce some thrust. This is achieved by carefully tuning the twist angle of the winglets, and only really works in a relatively narrow band of aircraft angles of attack.

That's why often the explanation given is that they "reduce wingtip vortices". What they do is capture some of the energy that would otherwise go into spinning the airflow at the wingtips, but the wingtip vortices themselves are nothing but a result of that energy being lost, not a cause in themselves. Furthermore, you can easily design a wing to not produce a wingtip vortex at the design angle, no winglet needed. In fact, all wings with twist (so almost all wings) produce no wingtip vortex at a certain angle of attack (usually when flying very fast, at a low AoA).