You can receive email notifications on Google Chrome, Firefox or Safari when you've signed into Gmail and have it open in your browser.
Note: You won't see any notifications if you've turned off all notifications for your browser.
Click on the Settings cog near the top-right corner of the Gmail screen
Choose See all settings
Scroll down to the Desktop notifications section
Click on the link to Enable desktop notifications
Click on Allow along the top of the screen
Select New email notifications on
To set a sound when new email is delivered, click on the Email notification sounds drop-down and choose a sound from the list
At the bottom of the page, click on Save Changes
If you use Windows 10, you will need to turn on Chrome notifications in the Windows 10 action centre.
To do this:
Click on the Action Centre icon in the task bar tray in the bottom-right corner of your screen
Choose Manage notifications at the top of the pane
Scroll down the Notifications & Actions screen to find Google Chrome
Turn this option On
Click on the close button in the top-right corner of the Notifications & Actions screen when complete