Availability of Aircraft Flight Manual
605.04 (1) No person shall conduct a take-off in an aircraft for which an aircraft flight manual is required by the applicable standards of airworthiness, unless the aircraft flight manual or, where established pursuant to Section 604.83 or Part VII, the aircraft operating manual is available to the flight crew members at their duty stations.
(2) The aircraft flight manual or, where an aircraft operating manual is established pursuant to Section 604.83 or Part VII, those parts of the aircraft flight manual that are incorporated into the aircraft operating manual shall include all of the amendments and supplementary material that are applicable to the aircraft type.
The wording makes it okay to lose your operating manual during flight: you just can't take off again. There's a good loophole. If you've forgotten your POH (pilot's operating handbook) also known as the AFM (aircraft flight manual) and you see the two guys in jackets coming across the tarmac, quickly agree on the phase of flight after take-off during which it fell out of the aircraft. And be on the phone to company to get a replacement.
There are aircraft that don't have operating manuals, I'd hazard a guess that if you build one in your garage it might not, and I've flown some old ones that had never had one, and a not as old as you might guess one that had an operating manual consisting of about eight mimeographed pages. (The mimeograph is an ancient duplication device falling in the historical timeline somewhere between carbon paper and the photocopier). Half of the pages dealt with the oxygen system (not installed). In a large airliner there's a whole shelf of ring binders that makes up the AFM. And yeah, you're supposed to have it on board, because then the passenger who has to land the aircraft during the climax of the movie can use it to look up the approach speed and the flap setting for landing. And you can look up fuel consumption figures for different altitudes, or settle arguments about what is on the circuit breaker labelled ALT FLD, or maybe ACI ECO depending on your interpretation of the font.