Edge used to support .epub (until October 2019), but doesn't anymore.
You can use the VitalSource Bookshelf app for .epub. Many textbook publishers make digital review copies available via VitalSource, so it's an app that some faculty may already have. VitalSource can be found in the Microsoft Store. For more information visit https://www.microsoft.com/en-us/p/vitalsource-bookshelf/9pczl8zkv9nx?activetab=pivot:overviewtab
For .mobi, please use the Kindle Reader app. This app is downloadable from Amazon, and requires no admin permissions to install. You can find information about the Kindle Reader at https://www.amazon.com/kindle-dbs/fd/kcp