I would like to ask suggestions for good texts which introduce circuit complexity. Any pointers to recent advances and open problems in this field would also be helpful.
Good text on introduction to circuit complexity
circuit complexity
To start off, there is of course Arora and Barak's book Computational Complexity: A Modern Approach. From there, parts 3 and 4 of Jukna's book Boolean Function Complexity: Advances and Frontiers make excellent reading material. Also, Ryan Williams teaches a nice course on circuit complexity whose course notes might hopefully be put up online :)