Extraordinary chemical and physical properties have been discovered from the studies of two-dimensional (2D) materials, ever since the successful exfoliation of graphene, the first 2D material. Theoretical investigations of electronic structure and spectroscopies of these materials play a fundamental role in deep understanding the various properties. In particular, the band structure and near-edge x-ray absorption fine structure (NEXAFS) spectroscopy can provide critical information near the Fermi level. In this thesis, we performed first-principles density functional theory calculations to study the electronic structure and NEXAFS spectra of four materials, including three 2D materials and one bulk material. The three 2D materials are atomically thin bismuth telluride, nitrogen and boron nitride doped graphenes. The bulk material is lithium intercalated graphite, an analogue of lithium doped graphene. Our studies provide important electronic property information of the studied materials, and are helpful for understanding their properties and developing potential applications.