We present high resolution (∼ 0.''2) 1.2 - 1.7 GHz (L-band) e-MERLIN observations of a LeMMINGs sub-sample consisting of 10 nearby, optically selected galaxies. The LeMMINGs project aims to study star formation at both L and C-bands (4 - 8 GHz) for a total of 286 galaxies with a median distance of 20 Mpc. The ten galaxies included in this thesis are a sub-sample of this project and comprise of the fourth observation block, in which each galaxy has been observed for a total of 40 minutes. Wide-field maps have been produced for each of the targets in order to search for any compact objects within the galaxy and the surrounding field. IC10 is included in the sub-sample of galaxies for this thesis. In this galaxy one HII region has been detected and imaged. There are no detections of any compact objects or extended emission within the other 9 target galaxies in this small sub-sample. Due to the high resolution of the e-MERLIN observations, much of the extended emission from the targets has been resolved out resulting in the low detection rate. In this thesis an analysis of the limits derived from these observations with respect to rates of star formation and AGN activity has been presented. It is concluded that low to moderate star formation rates of the galaxies studied here is consistent with the non-detection of compact radio emission from radio supernovae. No evidence for radio-emitting compact AGN components is found in any sources in this sub-sample. This is consistent with previous observations of these sources in the literature. It is hoped that future deep tier observations of IC10 will yield a higher number of detections for further analysis, but deeper observations are needed of the other 9 galaxies to study their radio and star-forming properties in greater detail.