Q: Can I download iTunes U on my mac?

You don't need to download the app on your Mac. Open iTunes, scroll to the very bottom, and under Explore, you will see iTunes U. Click on that, and the iTunes U window displays. It's the little cap and tassel icon at the top also - click on the three dots next to the icon that is displayed, and you will find it in the dropdown list. iTunes U is a part of iTunes.

https://www.apple.com/support/itunes-u/using/

Cheers,

GB

As I noted in my reply to

Will iTunes U ever be an App from the Mac App Store?

…the iTunes U student experience is only available for iOS.

The teacher experience is available on iOS and the web:

     https://itunesu.itunes.apple.com/coursemanager/

If you are a student, I suggest you tell Apple about your need for iTunes U on the Mac:

     http://www.apple.com/feedback/itunes-u_ios.html