We present the results of an extensive high-resolution imaging survey of M-dwarf multiplicity using the Lucky Imaging technique. The survey made use of the AstraLux Norte camera at the Calar Alto 2.2m telescope and the AstraLux Sur camera at the ESO New Technology Telescope in order to cover nearly the full sky. In total, 761 stars were observed (701M-type and 60 late K-type), among which 182 new and 37 previously known companions were detected in 205 systems. Most of the targets have been observed during two or more epochs, and could be confirmed as physical companions through common proper motion, often with orbital motion being confirmed in addition. After accounting for various bias effects, we find a total M-dwarf multiplicity fraction of 27% ± 3% within the AstraLux detection range of 008-6? (semimajor axes of ~3-227 AU at a median distance of 30pc). We examine various statistical multiplicity properties within the sample, such as the trend of multiplicity fraction with stellar mass and the semimajor axis distribution. The results indicate that M-dwarfs are largely consistent with constituting an intermediate step in a continuous distribution from higher-mass stars down to brown dwarfs. Along with other observational results in the literature, this provides further indications that stars and brown dwarfs may share a common formation mechanism, rather than being distinct populations.