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An easy way to learn to see those patterns is through exploring compiler output:
https://godbolt.org/
Other than that, I like "Assembly Language Step By Step" by Jeff Duntemann, which is currently in its third edition and is Linux-only, as opposed to previous editions which were MS-DOS and Linux. He has example assembly code for download on his website:
http://www.duntemann.com/assembly.html
My only annoyance is that apparently, even the most recent edition from 2009 is still 32-bit only.
Anyway, beyond that, you'd be looking for using assembly language to perform some specific task, like writing vectorized numerical code.