FAA has released updated editions of two key handbooks for pilots and flight instructors.
The new version of Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-25B) is a key reference for pilots training for the private pilot, commercial pilot, and flight instructor certificates.
You can find free PDFs of these handbooks and other FAA training manuals on the FAA website here and here.
The Pilot’s Handbook of Aeronautical Knowledge provides basic knowledge that is essential for pilots. This handbook introduces pilots to the broad spectrum of knowledge that will be needed as they progress in their pilot training. Except for the Code of Federal Regulations pertinent to civil aviation, most of the knowledge areas applicable to pilot certification are presented. This handbook is useful to beginning pilots, as well as those pursuing more advanced pilot certificates.
The Weight & Balance Handbook (FAA-H-8083-1B) is aimed at pilots and maintenance technicians.
The Aircraft Weight and Balance Handbook has been prepared in recognition of the importance of weight and balance technology in conducting safe and efficient flight. The objective of this handbook is twofold: to provide the airframe and powerplant mechanic (A&P) with the method of determining the empty weight and empty weight center of gravity (EWCG) of an aircraft and to furnish the flight crew with information on loading and operating the aircraft to ensure its weight is within the allowable limit and the center of gravity (CG) is within the allowable range.
You can find free PDFs of these handbooks and other FAA training manuals on the FAA website here and here.