The brain is composed of disparate neural populations that communicate and interact with one another. Although fiber bundles, similarities in molecular architecture, and synchronized neural activity all represent brain connectivity, a comprehensive study of how these connectivity modes jointly reflect brain structure and function remains missing. Here we systematically integrate seven multimodal, multiscale brain connectivity profiles derived from gene expression, neurotransmitter receptor density, cellular morphology, glucose metabolism, haemodynamic activity, and electrophysiology. We uncover a compact set of universal organizational principles through which brain geometry and neuroanatomy shape emergent connectivity modes. Connectivity modes also exhibit unique and diverse connection patterns, hub profiles, dominant gradients, and modular organization. Throughout, we observe a consistent primacy of molecular connectivity modes---namely correlated gene expression and receptor similarity---that map well onto multiple phenomena including the rich club and patterns of cortical abnormalities across 13 neurological, psychiatric, and neurodevelopmental disorders. Finally, we fuse all seven connectivity modes into a single multimodal network and show that it maps onto major organizational features of the brain including structural conenctivity, intrinsic functional networks, and cytoarchitectonic classes. Altogether, this work contributes to next-generation connectomics and the integrative study of inter-regional relationships.