How to make a backup of your email.

Download and install Mozilla Thunderbird.  https://www.thunderbird.net/en-US/

Set up your Thunderbird to access your UW email:  https://kb.wisc.edu/102005

Once you have done this, you should allow time for your Thunderbird client to access the email you have on the server.  

You should see, on the bottom of your mailbox list, something called Local Folders.

Local Folders allow you to download and store emails locally on your machine. 

You may want to consider creating a folder structure that makes sense for your Local Folders.

Your Local folders are stored on your machine in an mbox format, which is generally easy to import to other email clients.