Can someone tell me what is the font used by academia.SE?
It is very elegant.. Why it is not used throughout the stack exchange network?
This is a screenshot of what my browser renders.
For me the font for regular texts is Open Sans, questions in the question list are in Museo Slab – identified with Opera’s and Firefox’s Inspect Element tool. I strongly suspect (but cannot verify it right now) that this is loaded as a web font¹, so it should be the same for you, as long as your browser supports web fonts. PS: Looking at your screenshot, it almost certainly is Open Sans.
As to why this is not used all over the network: A font font should match the design, tone and topic of the site. For example, English Language uses a slab-serif font, which I suspect to be a trade-off between readability and feeling a little bit historical (and thus matching the design of that site). Open Sans would not be a good choice for that site in my opinion, as it is too modern. Also, using the same font all over the place eventually gets boring².
¹ At least one other Stack Exchange uses a web font.
² I, for example, have set my browser to auto-replace Arial (and similar) with another font, just because I got so tired of it.