Exploring the relationship between neuronal dynamics and ethologically relevant behaviour involves recording neuronal-population activity using technologies that are compatible with unrestricted animal behaviour. However, head-mounted microscopes that accommodate weight limits to allow for free animal behaviour typically compromise field of view, resolution or depth range, and are susceptible to movement-induced artefacts. Here we report a miniaturized head-mounted fluorescent mesoscope that we systematically optimized for calcium imaging at single-neuron resolution, for increased fields of view and depth of field, and for robustness against motion-generated artefacts. Weighing less than 2.5 g, the mesoscope enabled recordings of neuronal-population activity at up to 16 Hz, with 4 μm resolution over 300 μm depth-of-field across a field of view of 3.6 × 3.6 mm2 in the cortex of freely moving mice. We used the mesoscope to record large-scale neuronal-population activity in socially interacting mice during free exploration and during fear-conditioning experiments, and to investigate neurovascular coupling across multiple cortical regions.