The FAA provides a multitude of publications, free to the public.
These publications cover a wide array of topics such as basic aerodynamics, weather services, practical test standards, etc.
These documents are scattered through the FAA website. We have compiled links to some of these documents below.
Pilots handbook of aeronautical knowledge
Airplane Flying Handbook
Aircraft Weight & Balance Handbook
Aviation Weather services
Instrument Procedures Handbook
Instrument Flying Handbook
PTS Airplane (practical test standards)
Aeronautical chart users guide (VFR, IFR & IAP)
Aeronautical Information Manual (AIM)
Digital Airport/Facility Directory (A/FD)
Digital Terminal Procedures / Airport Diagrams (Approach Charts)
E-CFR Part 14 (Code of federal regulations)