The other day I was reading a paper on IEEE. To access the paper I needed to sign in through my institution. On the bottom of the paper, it read:
Accessed through [my institution name] at Oct 24, 9:30 PM
Will my institution be able to see all the papers I'm reading?
Your library will get aggregate data from the publishers along the lines of "in this month, 473 user sessions read 621 papers on the service". (The standard for this is COUNTER, and I assume IEEE use it). They won't be told "at 5.11 am on Sunday 20th, Steve downloaded..."
However, that data does exist, somewhere. If you are going through your university network there are situations in which it could in theory be identified from their logs, in much the same way that they could tell you then read a news story and finished for the day. The same is true for your home internet connection, but the widespread use of secure HTTPS connections make this level of detailed visibility less common than it used to be.
If you are signing in through Shibboleth authentication or similar, the university will know that you were authenticated for that provider at a particular time, but may not exactly know what items you read. (I would have to dig into the mechanism to be confident either way here). The publisher will also have a log of what you read, and that you were an authenticated user from X, but probably not precisely who you are.
It is vanishingly unlikely (and probably, in many jurisdictions, illegal) for this information to be used other than for things like troubleshooting and tracing abuse, however. So no-one is going to get sent a file of 'here's everything the department read this week, we highlighted Steve'.
But if there are problems, someone might well get an email that says 'user STEVE logged in from a weird looking Moldovan IP and downloaded 5000 papers in ten minutes last night, so the system then shut the account out, you should probably look into this before we reenable it'.
Since you are using your institution's network, yes, they could see all of your internet activity, including your accesses to the digital library of IEEE. But it is rather unlikely they would bother.
If your university wanted, they can use a man-in-the-middle attacks when establishing an SSL connection by using their own certificates. Some corporations with high security needs do this. They would need to get you to install a root certificate for this. Otherwise, they can tell the sites to which you go.
If you access the library via a token provided by the university via the log in through your institution, they can keep track of the token and its destination.
However, at least in the US, librarians will fight tooth and nails to dissuade the institution from getting this information while accessing library functions.
The counting statistics not only applies to publications (as in primary literature), but equally to databases your school then may highlight e.g., as top in a given specialty (example University of Vienna), most useful (example University of Geneva), or recommended (example Polytechnique Montréal). And if the electronic catalogue does not display these on the library's web site, beside the subscription fee, the number of accesses per license period and database still are arguments to (dis)continue the provision of access to all on campus' network, or only to the few interested groups of a department (perhaps especially if groups/schools do not team up).
Yes they can.
Your institutional library uses data on what papers you're reading to decide which journals to subscribe to.
