I think it is important to learn jQuery if you are going to use jQuery Mobile.
I highly recommend "jQuery Pocket Reference" by David Flanigan. It is just enough jQuery to go with jQuery Mobile. The one thing it is missing is coverage of Promises. Learning jQuery is more comprehensive, but I find the book I almost always turn to is jQuery Pocket Reference.
That said, the online documentation for jQuery is as good as the online documentation for jQuery Mobile is bad. That is to say, it is an excellent reference, and there is a discussion area at the bottom of every page that helps clarify anything that is not completely clear. If you learn well from references, then the online jQuery documentation may be all that you need. For myself, I think that the way that jQuery Pocket Reference is organized is valuable, especially it's chart on DOM modification methods.
I think you are better off learning the two together, and there is actually some advantage to not having known jQuery previously. You will avoid a lot of common mistakes, because I think a lot of new JQM developers make incorrect assumptions and do not read the JQM documentation in enough depth to understand how different it is from common web programming.
It is a framework which has some restrictive rules, and you have to live within those rules. It is not just a pretty face that will instantly make your site look good by loading a CSS and a JS file and start sprinkling your pages with a few data- attributes, and then continue doing everything else the way you had. Unfortunately, way too many developers take this approach and then wonder why things do not work the way they had expected.
Unless you also intend to use jQuery UI in other projects, you can skip anything on jQuery UI when you study jQuery, as it will only lead to confusion.
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