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Is it critical that all pilots know them both inside and out?
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Not necessarily inside and out, but the parts that apply to the type of flying you do- yes, I'd say so. You can never know too much! The AIM is a good read for the middle of winter when there's nothing else to do (if you live in the cold climates, that is). I've read it cover-to-cover twice (damn NY winters!)
Although the Texas summers have the same effect on my desire to spend time outside...
Viper, a lot of the FAR stuff won't apply to you for a while to come, but the parts that it would be good to get familiar with are FAR Parts 1, 61, 91, and perhaps 141 if you plan to attend a 141 school.
The AIM is all good stuff, cover to cover. I got a kick out of 7-6-4