No, you cannot legally fly a certified aircraft without a valid Airplane Flight Manual (AFM) on board. According to FAA and EASA regulations, the AFM (or in some smaller/older aircraft, the Pilot’s Operating Handbook/POH) is considered a required document for flight. Specifically, the "limitations" section of the AFM is legally binding, and the manual must be specific to that exact aircraft's serial number and current equipment configuration. The AFM contains critical data such as weight and balance limits, airspeeds for various maneuvers, emergency procedures, and performance charts that a pilot may need to consult during flight. In modern aviation, many regulators allow for "Electronic Flight Manuals" on devices like iPads (Electronic Flight Bags), provided they meet strict battery and accessibility requirements, but the content must still be present and accessible. Flying without the AFM is a violation of the aircraft’s Type Certificate and can lead to significant legal penalties, the grounding of the aircraft, and the voiding of insurance coverage in the event of an incident. It is one of the "AROW" documents (Airworthiness, Registration, Operating Handbook, Weight and Balance) that every pilot must verify before engine start.