In elementary OS, you will see the notification messages on the top right corner of the screen. Although it is useful for email and for some important programs, the notifications are turned ON by default settings and every installed program will get notification rights once installed. Thankfully, there is a easy way to control the notifications.
STEP 1: Launch “System Settings” by clicking on the “Power” icon > “System Settings”.
STEP 2: Click “Notifications” in the “Personal” section.
STEP 3: In the left pane, you can scroll through each and every program that has notification rights. You will not see all programs listed here, just because not all programs have notification intent. Select the program for which you want to turn off notifications and then toggle the “Sounds” and “Bubbles” to OFF position. You do have option to only turn OFF Sounds and keep the bubble notifications if you want it that way.
STEP 4: Optionally, you can disable notifications completely by enabling the “Do Not Disturb” on the bottom left of the Notifications dialog box. It will still show the important system notifications like volume, display brightness, and other elementary OS system related messages which are important to keep your computer running smoothly. It will only turn off notifications for third-party applications installed in your computer including Geary email.