Mammalian cortex features a vast diversity of neuronal cell types, each with characteristic anatomical, molecular and functional properties. Synaptic connectivity powerfully shapes how each cell type participates in the cortical circuit, but mapping connectivity rules at the resolution of distinct cell types remains difficult. Here, we used millimeter-scale volumetric electron microscopy1 to investigate the connectivity of all inhibitory neurons across a densely-segmented neuronal population of 1352 cells spanning all layers of mouse visual cortex, producing a wiring diagram of inhibitory connections with more than 70,000 synapses. Taking a data-driven approach inspired by classical neuroanatomy, we classified inhibitory neurons based on the relative targeting of dendritic compartments and other inhibitory cells and developed a novel classification of excitatory neurons based on the morphological and synaptic input properties. The synaptic connectivity between inhibitory cells revealed a novel class of disinhibitory specialist targeting basket cells, in addition to familiar subclasses. Analysis of the inhibitory connectivity onto excitatory neurons found widespread specificity, with many interneurons exhibiting differential targeting of certain subpopulations spatially intermingled with other potential targets. Inhibitory targeting was organized into "motif groups," diverse sets of cells that collectively target both perisomatic and dendritic compartments of the same excitatory targets. Collectively, our analysis identified new organizing principles for cortical inhibition and will serve as a foundation for linking modern multimodal neuronal atlases with the cortical wiring diagram.