While algebraic topology is now well established as an applicable branch of mathematics, its emergence in neuroscience is surprisingly recent. In this talk I will present a summary of an ongoing joint project with mathematician and neuroscientists. I will start with some basic facts on neuroscience and the digital reconstruction of a rat’s neocortex by the Blue Brain Project in EPFL. I will then explain how data emerging from this reconstruction can be mapped into abstract graphs that in turn give rise to certain mathematical objects in the realm of algebraic and combinatorial topology. Following a short introduction to some of the basic tools of algebraic topology, I will explain how they can potentially be used in the context of neuroscience. Having set up the scene, I will proceed by presenting the results of an ongoing collaboration with the Blue Brain Project team. In particular I shall demonstrate how the topological techniques give new insights on the behaviour of neural systems and inspire new directions in neuroscience research.