Named after Pope Gregory, Pontifical Gregorian University is the most prestigious university run by the Catholic Church. It is to the Vatican what the Sorbone is to France, Oxford to England, or Harvard to the US.

While located in downtown Rome (if there is something like "downtown" in Rome), it is technically part of the Vatican State, a fact that was used, among other things, to help Jews during World War II. Any time a Jew chased by the Nazi ran into the University, the Nazi had to ask permission to go after him. It so happened that every single time the Rector (that is, the Chancellor as they are called in the US) was hard to find until the moment the refugee was safely gone through the back door. At that moment, the Rector was found and gave the required permission to search the premises (and thus to give the refugee more time to disappear).

The faculty of Gregorian University is almost exclusively chosen from the members of the Jesuit order (originally completely exclusively), though the student body is a mix of members of various orders, secular priests, even lay people, and lately even non-Catholics, from all over the world. The teachings depend on the faculty - some members are conservative, though most are quite liberal (hey, they are Jesuits, after all).

Except for Faculty (i.e. Department) of Canon Law, all lectures are in Italian. The Canon Law lectures are in Latin - the last school to still do it - the reasoning being that a Canonist who can read the Code of Canon Law in its original language (Latin) has always an upper edge over one who can not (i.e., he can argue, yes, I see what you are saying, but you are basing your interpretation on a translation, while the Latin original really means such and such thing).

So many Catholic bishops are Gregorian graduates that there is a bulletin board in the lobby of the University which always says "Another Gregorian graduate named bishop" and lists the most recent nominees.

How do I know all that? Guess what, I've got a JCL (graduate degree in Canon Law) from the Greg (as it is often called by American students. Not that it does me any good now that I am a Buddhist...