FAA's official manuals for the private pilot license is this book, Airplane Flying Handbook which covers the practical skills and Pilots Handbook of Aeronautical Knowledge which covers the knowledge requirement. All questions from the FAA written and oral exams come from the relevant sections of these books. (Your requirements for the practical checkride are covered by the Private Pilot Airman's Certification Standards.)
This handbook introduces the basic skills and knowledge essential for piloting airplanes. It benefits student pilots just beginning their aviation endeavors, as well as pilots preparing for additional certificates and ratings or who want to improve their flying proficiency and flight instructors engaged in teaching pilots of all skill levels.
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