There are a number of topics that an Aviation Maintenance Technician, or Airframe & Powerplant mechanic studies, seperated into three major categories.
Each has their own subtopics.
The following are the chapters from FAA's 8083 General textbook, which is becoming the main textbook taught in FAR Part 147 AMT schools.
The subjects under Airframe, taken from the contents of Aviation Maintenance Technician Handbook - Airframe (FAA-H-8083-31)
Requirements of an aircraft engine:
Types of engines: Opposed (O type,) V-type, Radial Engines
Design and construction of reciprocating engines; it's parts. The basic major components of a reciprocating engine are the crankcase, cylinders, pistons, connecting rods, valves, valve-operating mechanism, and crankshaft.
Aircraft engines are divided into sections: nose, crankcase and accessory section.
The crankcase is the foundation of the engine and is usually made out of cast or forged aluminum and is the main support of the entire engine. The engine mounts connect the crankcase to the aircraft. It split into 2 halves that hold the crankshaft and camshaft between them with the nose at the front and the accessory case mounted to the rear. The separate cylinders are mounted to the crankcase on precisely machined surfaces that cylinders are mounted to are called cylinder pads. On the typical opposed engine, the cylinders are mounted to the side, and the induction system manifold connected to the bottom.
The crankcase accessory section is a separate section at the rear can be one piece with means for mounting the accessories, such as magnetos, carburetors, fuel, oil, vacuum pumps, starter, generator, tachometer drive, etc. required to run the engine or use the engine output to drive other systems like the electrical system. The accessories are driven by gears.
The front nose section on the crankcase is where the propeller mounts either directly to an attachment on the end of the crankshaft, or via a set of reduction gears and a propeller governor for high powered engines.
A modern aircraft engine has electronic controls that that accurately control the flow of fuel to the engine. See FADEC
The basic parts of a fuel system include tanks, boost pumps, lines, selector valves, strainers, engine-driven pumps, and pressure gauges. Aviation fuel is covered in the general section
Aviation Mechanic testguide – General, Airframe, and Powerplant (PDF)
CFR 14:Part 65 CERTIFICATION: AIRMEN OTHER THAN FLIGHT CREWMEMBERS Subpart D—Mechanics