This talk will present theoretical studies of electronic structure of Fe-based superconductors. It will first establish the basic spin/orbital correlation of the parent compound [1] that is now known to also persist in the doped superconducting samples. It will then discuss the rich magnetic correlation in the families [2], followed by our recent finding of surprising effects of nesting of the itinerant electrons [3]. Finally, the talk will discuss the novel physical effects of the glide translational symmetry of the system on the electronic structure [4] and the novel pairing structure [5], highlighting a new class of superconducting state. I will leave the topic of novel physical effects due to disordered impurities [6-9] to private discussion after the talk.

1. Chi-Cheng Lee, Wei-Guo Yin, and Wei Ku, Phys. Rev. Lett. 103, 267001 (2009).
2. Wei-Guo Yin, Chi-Cheng Lee, and Wei Ku, Phys. Rev. Lett. 105, 107004 (2010).
3. Yuting Tam, Daoxin Yao, and Wei Ku, unpublished.
4. Chia-Hui Lin, et al, Phys. Rev. Lett. 107. 257001 (2011).
5. Chia-Hui Lin, et al, arXiv:1403.3687
6. Tom Berlijn, P. J. Hirschfeld, and Wei Ku, Phys. Rev. Lett. 109, 147003 (2012).
7. Tom Berlijn, et al, Phys. Rev. Lett. 108, 207003 (2012).
8. Limin Wang, et al, Phys. Rev. Lett. 110. 037001 (2013).
9. Tom Berlijn, et al, Phys. Rev. B 89, 020501(R) (2014).