We have already shown you how to disable notifications for the Metro mail app, but the majority of users will still be using Outlook.
How to Disable Desktop Notifications in Outlook 2013
The first thing you will need to do is open Outlook and click on File to enter the Backstage view.
Now head into the Options section by selecting it from the left hand pane.
From here you will want to select Mail.
Now you will need to scroll down to the Message arrival section and uncheck the Display a Desktop Alert check box.
That’s all there is to it.