The understanding of brain computations requires methods that read out neural activity on different spatial and temporal scales. Following signal propagation and integration across a neuron and recording the concerted activity of hundreds of neurons pose distinct challenges, and the design of imaging systems has been mostly focused on tackling one of the two operations. We developed a high-resolution, acousto-optic two-photon microscope with continuous three-dimensional (3D) trajectory and random-access scanning modes that reaches near-cubic-millimeter scan range and can be adapted to imaging different spatial scales. We performed 3D calcium imaging of action potential backpropagation and dendritic spike forward propagation at sub-millisecond temporal resolution in mouse brain slices. We also performed volumetric random-access scanning calcium imaging of spontaneous and visual stimulation-evoked activity in hundreds of neurons of the mouse visual cortex in vivo. These experiments demonstrate the subcellular and network-scale imaging capabilities of our system.