It's a Linksys n wireless USB adapter (in case that matters).
Should work if the Apple router is fairly recent. But there are almost always issues, if only because networking manufacturers use standard industry terminology for things like wireless security types and Apple, well....they don't.
So, start by disabling wireless security in the Apple device and only try applying it once you have established a reliable connection. Also pay attention to wireless mode settings in the router -- you may have to experiment with those.