The success of diffusion MRI is deeply rooted in the fact that during their micrometric random displacements water molecules explore tissue microstructure. Hence by labeling magnetically spins of displaced water, diffusion MRI provides us with exquisite information about the sizes and orientations on the multiple compartments present inside an imaging voxel. Through the causal relation between on one hand the imaged restricted and oriented water mobility and on the other hand the axonal orientations in brain white matter, diffusion MRI has become a powerful method to infer fiber tract architecture and brain anatomic connectivity. This work is not only a journey that takes us from essential diffusion MRI physics to an investigation of the brain neuronal circuitry, but also a thesis aiming at demonstrating the power of large scale analysis of brain connectivity, where every technological component is essential. After a short introduction on molecular diffusion and diffusion NMR, we start by showing that diffusion contrast is positive. This key issue that was only postulated up to now, allows us to justify why diffusion can be computed accurately with the only signal modulus. Accordingly, various emerging MRI techniques that map non-Gaussian diffusion have found a sound justification. In particular it is precisely the result that allows us to map distribution of diffusion related spin displacements by Fourier transformation of the measured signal modulus, hence to do Diffusion Spectrum MRI. We show through multiples MR experiments how the shape of this distribution in a complicated multi-compartment biological system can be measured and how its characteristic local heterogeneity is a mirror of fiber architectures. We discuss in detail its interpretation and its relation to other diffusion MRI techniques. Tractography is the necessary link that from diffusion MRI provides us with nerve fiber trajectories and maps of brain axonal connectivity. In this thesis two algorithms are proposed, while the first is designed for diffusion tensor MRI, the second is shaped for high angular resolution diffusion MRI and specifically tested on Diffusion Spectrum MRI. After having considered the potentials and the limitations of these line generation algorithms, we investigate whether tractography can be formulated as a segmentation problem in a high dimensional non Euclidean space, i.e. position-orientation space. With the help of the developed tools we address some key neuro-scientific questions. Based on diffusion tensor MRI data of 32 healthy volunteers, language networks are investigated. It is shown that right-handed men are massively interconnected between the left-hemisphere speech areas whereas the homologous in the right hemisphere are sparse; furthermore interhemispheric connections between the speech areas and their contralatera1 homologues are relatively strong. Women and left-handed men have equally strong intrahemispheric connections in both hemispheres, but women have a higher density of interhemispheric connections. After this quantitative study, Diffusion Spectrum MRI data of a single subject is collected and tractography performed in order to analyze the global connectivity pattern of the human brain. For this purpose we propose to model this large scale architecture by an abstract graph. It is shown that the long-range axonal network exhibits a "small world" topology. This type of particular architecture is present in various large scale communication networks. They emerge usually from a growing process where optimal communication has to be developed under some resource constraints. Furthermore we show also that the architecture of axonal connectivity between cortical areas exhibits a hierarchical organization. These results, which confirm more indirect studies, provide essential material to discuss not only brain evolution and development but also information processing at the level of the brain.