THE REQUIREMENT FOR CLOSER TOLERANCES OF FLAT SURFACES IS BECOMING MORE IN DEMAND. IN ADDITION, NEW MATERIALS ARE BEING DEVELOPED WHICH OFTEN PRESENT PROBLEMS FOR MORE TRADITIONAL MACHINING PROCESSES. THIS PAPER DESCRIBES THE PROCESS OF PRECISION ABRASIVE MACHINING FLAT SURFACES IN A CONTROLLED PRODUCTION MANNER. THE PROCESS IS APPLICABLE TO ALMOST ANY STABLE MATERIAL SUCH AS FERROUS AND NONFERROUS METALS, CERAMICS, PLASTICS, CRYSTALS, ALLOYS, AND VARIOUS SINTERED PRODUCTS. THREE DIFFERENT PROCESSES ARE COVERED. THE FIRST IS LOOSE ABRASIVE MACHINING, ALSO KNOWN AS LAPPING. THE SECOND IS BONDED ABRASIVE MACHINING, ALSO KNOWN AS FLAT HONING AND FINE GRINDING. THE THIRD PROCESS IS PRECISION POLISHING USING LOOSELY HELD OR IMBEDDED ABRASIVE TO PRODUCE EXTREMELY FLAT REFLECTIVE SURFACES.