Over the past several years, research at the interface of topology and neuroscience has grown remarkably fast. Topology has, for example, been successfully applied to objective classification of neuron morphologies and to automatic detection of network dynamics. In this talk I will focus primarily on the algebraic topology of brain structure and function, describing results obtained by members of my lab in collaboration with the Blue Brain Project on digitally reconstructed microcircuits of neurons in the rat cortex. I will also describe our on-going work on the topology of synaptic plasticity. The talk will include a brief overview of the Blue Brain Project.