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JQuery is an easy to use framework for special effects with Javascript, and JQuery UI is a separate framework that provides many UI elements like calendars and buttons.
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Pros
Pro Flexible because of countless plugins
One of jQuery's main strengths is it's flexibility. It's very easy to find and add jQuery plugins for almost every problem you might have. This is extremely helpful in lowering development time and avoids the need to reinvent the wheel and find solutions that have already been found.
Pro Great learning resources
JQuery is undoubtedly the largest JavaScript library and one of the most important tools in web development. As such. it has a massive number of guides and tutorials out there for almost every aspect of development using JQuery. The official documentations is also excellent for beginners and experienced users alike.
Cons
Con Spaghetti code
jQuery's biggest strength is also one of it's biggest weaknesses. The fact that it's easy to use makes it also extremely easy to write long massive JavaScript files filled with spaghetti code.
jQuery is designed to help with DOM transverses and CSS selectors. It's amazingly efficient at this. Unfortunately it's not designed to be used as a Framework for full client-side interaction. jQuery CSS selectors if used incorrectly can become impossible to maintain. If you consider callbacks, cosmetic changes and arbitrary names, it can become impossible to maintain a jQuery file.