POH library

Finding the right handbook is harder than it should be. A 1978 172N and a G1000 172S share a type certificate and almost nothing else that matters for numbers. This is a directory of where each variant's handbook actually lives, with an honest note on what you are downloading.

Every link here goes to somebody else's site. Use them to study. The current, revision-controlled POH or AFM in your aircraft, with its own weight and balance and equipment list, is the only document that governs a flight.

Aircraft photography via Wikimedia Commons — full credits on each aircraft's checklist page.

FAA handbooks (free)

U.S. government works, so these are public domain: download them, print them, hand them to a student. No manufacturer copyright to worry about. The FAA moves file paths around, so these point at landing pages where one exists.

Pilot's Handbook of Aeronautical KnowledgeFAA-H-8083-25C
The ground-school book. Chapter 10 explains how to read a POH and what each section is for, which is where to start if a handbook feels opaque.
Airplane Flying HandbookFAA-H-8083-3C
Technique: takeoffs, landings, stalls, emergencies. Per-chapter PDFs, because the full book runs well over 200 MB.
Aircraft Weight and Balance HandbookFAA-H-8083-1B
How to run a real loading problem, including what to do when the equipment list in the POH no longer matches the airplane.
Instrument Flying HandbookFAA-H-8083-15B
Instrument technique and systems. Pairs with the Instrument Procedures Handbook for the chart and procedure side.
Instrument Procedures HandbookFAA-H-8083-16B
Departures, arrivals, approaches, and the ATC side of an IFR flight.
Risk Management HandbookFAA-H-8083-2A
Personal minimums and decision-making frameworks. Short, and the most useful thing on this list for a low-time pilot planning a long trip.
Aviation Weather HandbookFAA-H-8083-28B
The consolidated weather reference that replaced AC 00-6 and AC 00-45. Product decoding lives here now.
Aviation Instructor's HandbookAIH
For CFIs and CFI candidates. Also useful if you are building training material or briefing checklists for a club.
PHAK, AFH, and Weight and Balance MOSAIC addendaMOSAIC addenda
The FAA published addenda rather than reissuing the handbooks for the MOSAIC light-sport rule changes. Read the addendum alongside the parent handbook, not instead of it.
All FAA aviation handbooks and manualsIndex
The FAA's own index page. Go here first when a direct link below has moved, because they do move.

Building a card for one of these? Start from a checklist template and cross-check every line against the handbook you just found.