This thesis presents the results of a survey of 913 M-dwarf stars from the Lepine and Shara Proper Motion (LSPM) catalog within 33 parsecs. Data for these targets was collected with the Robo-AO camera on the Palomar 60” telescope. In order to determine which stars were in bound systems, the images with multiple stars, first observed in 2012, were observed again in 2014 to examine changes in separation and position angles. Stars with little change in position with respect to one another suggest they are common proper motion pairs. The Washington Double Star (WDS) catalog and other resources were used to further determine binarity. This research was conducted to improve upon the statistics of nearby multiple M-dwarf systems. Identifying and confirming multiple systems at both wide and small separations will improve our understanding of M-dwarf formation by comparing these results to existing star formation models.

This paper includes a re-examination the coeval, multiple dwarf system Glies 569 in order to resolve the contradictory findings in the area of age. Absolute magnitudes in the f I and K bands are calculated, and are analyzed along with newly obtained dynamic mass estimates for the B components as well as other attributes of this system that have been well established in the literature. Ages are inferred by the placement of these objects on a variety of HR diagrams_ using the evolutionary models of Baraffe et al. These results strengthen the case for a possible third member of the Bab component of Gliese 569. The system's age is probably in the range of 100 to 500 million years; however, a more specific age estimate cannot yet be concluded. Because of the uncertainty associated with the dynamical mass estimates for the B component, the error bars associated with the age estimates are considerable. Finally, future research is suggested to better understand this hierarchical multiple system.