Enable Notifications for Google Calendar Events:

 

1.  Click "Calendar" at the top of the Gmail window.

2.  Click the cog icon in the top right corner and click "Calendar settings".

 

3.  Click "Calendars" in the gold-colored bar.

 

4.  Click your name, it should be listed first in the "My Calendars" section.

5.  Click "Notifications" in the gold-colored bar.

 

6.  Make sure the email options are checked for new, changed, and canceled invitations then click "Save".

 

You should get email notifications now for new calendar events you are invited to. 

The attached downloadable PDF includes screenshots.