High-resolution Al L-2,L-3-edge x-ray absorption near edge structure (XANES) spectra have been measured in selected materials containing aluminium in 4-, 5- and 6-coordination. A shift of 1.5 eV is observed between the onset of Al- and Al- L-2,L-3-edge XANES, in agreement with the magnitude of the shift observed at the Al K- edge. The differences in the position and shape of low-energy components of Al L-2,L-3-edge XANES spectra provide a unique fingerprint of the geometry of the Al site and of the nature of Al-O chemical bond. The high resolution allows the calculation of electronic parameters such as the spin-orbit coupling and exchange energy using intermediate coupling theory. The electron-hole exchange energy decreases in tetrahedral as compared to octahedral symmetry, in relation with the increased screening of the core hole in the former. Al L-2,L-3-edge XANES spectra confirm a major structural difference between glassy and crystalline NaAlSi2O6, with Al in 4- and 6-coordination, respectively, Al coordination remaining unchanged in NaAl1-xFexSi2O6 glasses, as Fe is substituted for Al.