1. Introduction
2. Survey of Planetary Nebulae in M31
2.1. Survey Characteristics
2.2. Substructures in M 31 and their PN Sub-samples
2.3. Extinction in the M31 Survey Region
3. The Planetary Nebula Luminosity Function
3.2. Independent Calibration to a Large PN Sample
3.3. Cumulative PNLFs of the M 31 Regions
3.4. Comparison of the Shapes of the PNLFs
3.5. Quantitative Differences of the PNLFs of Distinct Subregions in M31
4. Cumulative PNLFs and Stellar Populations in the M31 Disc and Inner Halo
4.3. Stellar Population Dominating the Very Faint-end of the PNLF
5. Discussion
5.2. The Merger Origin of the Inner-halo Substructures in M 31
6. Conclusions