FAA's official manuals for the private pilot license are this book, Pilots Handbook of Aeronautical Knowledge which covers the knowledge requirements and Airplane Flying Handbook which covers the practical skills. All questions from the FAA written and oral exams come from the relevant sections of these books. (Standards for the practical checkride are covered by the Airman Certification Standards.)
Pilots Handbook of Aeronautical Knowledge provides basic knowledge essential for all pilots; from beginning student pilots to those pursuing more advanced pilot certificates this book introduces pilots to the broad spectrum of knowledge needed as they progress through pilot training.
The book begins with a basic introduction to flying, including the history of flight, the role of the Federal Aviation Administration (FAA), criteria for earning the various pilot certificates, how to select a flight school and instructor, and the tests associated with earning a pilot certificate.
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