This work focuses on two complementary aspects of magnetic source imaging using Magnetoencephalography: 1. Imaging of neural current sources from MEG surface recordings. 2. Dynamic characterization of neural current patterns at the surface of the cortex. MEG Source Imaging Accurate estimation of the local spatial extent of neural current activity is very important for the quantitative analysis of neural current sources, as estimated from Magnetoencephalography (MEG) surface recordings. In association with the excellent time resolution offered by MEG, this would represent a major advancement in non invasive, time-resolved functional brain imaging. We address this issue through a new method called Multipole Cortical Remapping (MCR) to accurately specify the spatial extent of neural current sources. In MCR, the zero-order Tikhonov regularized image of the current distribution on the cortex is rst estimated from MEG surface data for which we sought for a realistic model of neural generators. Then the resulting functional image is thresholded using a simple histogram-based principle. This thresholded image is then decomposed into groups of activation patterns following an automatic labeling algorithm based on the geometrical properties of the cortical surface. The equivalent multipolar decomposition of each current patch is then obtained. By default, the multipolar moments are not readily related to the actual anatomical support of the actual neural currents detected using MEG. Hence we introduce an image remapping techniques of the multipolar parameters back onto the original cortical manifold in a Bayesian framework that includes physiological and anatomical priors. MEG Source Dynamic Characterization For dynamic characterization of neural current patterns at the surface of the cortex, we used modied Helmholtz Hodge Decomposition (HHD) which is applied on motion eld of neural current sources. This motion eld is also known as optical ow. Optical ow is the apparent motion due to variations in the pattern of brightness and, under specic conditions, may mimic the velocity eld of an object. Normally, the optical ow is obtained in a two-dimensional domain, which may prevent access to some essential features of the object's motion with respect to the topology or geometry of the domain onto which it is evolving. A new variational method to represent optical ow on non at surfaces using Riemannian formulation was recently introduced by our group to overcome this issue. We broaden this framework and introduce a new formalism to detect features in the resulting optical ow model using a modied and extend framework to the HHD on 2-Riemannian manifolds, which we use to characterize neural current sources. HHD is a technique used to decompose a two-dimensional (resp. threedimensional) continuous vector eld into the sum of 3 distinct components: 1. a non-rotational element, deriving from the gradient of a scalar potential U; 2. a non-diverging component, deriving from the rotational of a scalar potential A (resp. vectorial potential); 3. a harmonic vectorial part, i.e., whose Laplacian vanishes The HHD approach enables the decomposition and tracking of time-resolved neural current ows as obtained from MEG source imaging as sources and sinks, e.g., by detecting relative maxima of the non-rotational scalar potential. It also extends the analysis of brain activity in terms of tracking travelling objects onto the cortical manifold by detecting vectors of largest amplitudes in zero Laplacian harmonic vector elds. We also apply HHD in structural and functional brain imaging applications. The results are very encouraging. We believe that HHD has an enormous potential and it can decipher many riddles in neuroscience. The methods discussed in HHD portion of the thesis are implemented in Matlab as plug-in to the Brainstorm (MEG/EEG data processing software) and can be downloaded from: http://neuroimage.usc.edu/brainstorm