The electron energy loss near edge structures (ELNES) appearing in an electron energy loss spectrum obtained through transmission electron microscopy (TEM) have the potential to unravel atomic and electronic structures with sub-nano meter resolution. For this reason, TEM-ELNES has become one of the most powerful analytical methods in materials research. On the other hand, theoretical calculations are indispensable in interpreting the ELNES spectrum. Here, the basics and applications of one-particle, two-particle and multi-particle ELNES calculations are reviewed. A key point for the ELNES calculation is the proper introduction of the core-hole effect. Some applications of one-particle ELNES calculations to huge systems of more than 1000 atoms, and complex systems, such as liquids, are reported. In the two-particle calculations, the importance of the correct treatment of the excitonic interaction is demonstrated in calculating the low-energy ELNES, for example at the Li-K edge. In addition, an unusually strong excitonic interactions in the O-K edge of perovskite oxides is identified. The multi-particle calculations are necessary to reproduce the multiplet structures appearing at the transition metal L2,3-edges and rare-earth M4,5-edges. Applications to dilute magnetic semiconductors and Li-ion battery materials are presented. Furthermore, beyond the 'conventional' ELNES calculations, theoretical calculations of electron/X-ray magnetic circular dichroism (MCD) and the vibrational information in ELNES, are reported.