The complete condensation kinetics of three silicon alkoxides have been studied by 29 Si NMR in the conditions of rapid hydrolysis (acidic medium, water in excess). The gelation of the tetravalent TEOS takes several weeks, whereas the trivalent MTEOS and VTEOS do not form gels. From a quantitative data analysis, we deduce that the first steps of the condensation proceed by progressive formation of small organized units. This accounts for the occurence of highly condensed agglomerates, the absence of gelation in trivalent systems and the very slow kinetics (logarithmic function of time). For the tetravalent TEOS, this is followed by an aggregation phase, which leads to gelation. After the gel time, the transformation of the sol fraction into gel has been followed by observing the broadening of the static NMR spectra. Moreover, the structures of the aerogels obtained by hypercritical drying and of the densified materials resulting from further sintering are characterized by MAS NMR. In particular, measurements of the nuclear relaxation in samples doped with paramagnetic impurities give directly the fractal dimension D of the silicate lattice. The measured value is in agreement with that obtained by the SAXS technique in aerogels (D≈2.2) and is close to D=3 for the densified materials.