JQuery is widely used. Google, Netflix, Microsoft, and Nokia are just a few examples of big names that use JQuery. So, it is compatible with all major browsers. This means, when you create something it should be compatible with pretty much all computers and devices. And, good programs should make their code as compatible as they can.
JQuery is released under an MIT license. I personally don’t know much about the MIT license, but I do know it is GPL compatible, which is a good thing.
I’m currently working on a video series teaching the basics of JQuery. Later on I’ll move on to JQuery Mobile and how to package your programs for use on different OS’s including making basic APK files for your Android devices.