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The human cerebral cortex consists of approximately 1010 neurons that are organized into a complex network of local circuits and long-range connections. During the past years there has been an increasing interest from the neuro-scientific community towards the study of this network, referred to as the human connectome. Due to its ability to probe the tissue microstructure in vivo and non invasively, diffusion MRI has revealed to be a helpful tool for the analysis of brain axonal pathways at the millimeter scale. Whereas the neuronal level remains unreachable, diffusion MRI enables the mapping of a low-resolution estimate of the human connectome, which should give a new breath to the study of normal or pathologic neuroanatomy. After a short introduction on diffusion MRI and tractography, the process by which fiber tracts are reconstructed from the diffusion images, we present a methodology allowing the creation of normalized whole-brain structural connection matrices derived from tractography and representing the human connectome. Based on the developed framework we then investigate the potential of front propagation algorithms in tractography. We compare their performance with classical tractography approaches on several well-known associative fiber pathways, and we discuss their advantages and limitations. Several solutions are proposed in order to evaluate and validate the connectome-related methodology. We develop a method to estimate the respective contributions of diffusion contrast versus other effects to a tractography result. Using this methodology, we show that whereas we can have a strong confidence in mid- and long-range connections, short-range connectivity has to be interpreted with care. Next, we demonstrate the strong relationship between the structural connectivity obtained from diffusion MR tractography and the functional connectivity measured with functional MRI. Then, we compare the performance of several diffusion MRI techniques through connectome-based measurements. We find that diffusion spectrum imaging is more sensitive and therefore enhances the results of tractography. Finally, we present two network-oriented applications. We use the human connectome to reveal the small-world architecture of the brain, a very efficient network topology in terms of wiring and power supply. We identify the cortical areas that belong to the core of structural connectivity. We show that these regions also belong to the default mode network, a set of dynamically coupled brain regions that are found to be more highly activated at rest. As a conclusion, we emphasize the potential of human connectome mapping for clinical applications and pathological studies.