A catalog of neuronal cell types has often been called a "parts list" of the brain, and regarded as a prerequisite for understanding brain function. In the optic lobe of Drosophila, rules of connectivity between cell types have already proven essential for understanding fly vision. Here we analyze the fly connectome to complete the list of cell types intrinsic to the optic lobe, as well as the rules governing their connectivity. We more than double the list of known types. Most new cell types contain between 10 and 100 cells, and integrate information over medium distances in the visual field. Some existing type families (Tm, Li, and LPi) at least double in number of types. We introduce a new Sm interneuron family, which contains more types than any other, and three new families of cross-neuropil types. Self-consistency of cell types is demonstrated through automatic assignment of cells to types by distance in high-dimensional feature space, and further validation is provided by algorithms that select small subsets of discriminative features. Cell types with similar connectivity patterns divide into clusters that are interpretable in terms of motion, object, and color vision. Our work showcases the advantages of connectomic cell typing: complete and unbiased sampling, a rich array of features based on connectivity, and reduction of the connectome to a drastically simpler wiring diagram of cell types, with immediate relevance for brain function and development.