Turn off email notifications

Facebook

Facebook sends you email to your primary email address they have for you whenever you get a post, or some other type of notification. If you have it set to notify you on any event, your email will get full of replies. These replies are from Facebook and not from the group or page that you are a member of.
If you do not want to get notification whenever someone posts on a page or group your involved in, you can set it up to only give you Summary and important updates only. When you set it to summary and important updates only, you will get much less email. However there is no way to completely turn off email notifications entirely.

To change notification to summary and important updates instead of an email whenever someone posts, do the following.

Open Facebook
Click Down Arrow

Click Settings

Click Notifications

To the right of Email, click Edit

Here is the options you have
1. WHAT YOU'LL RECEIVE
  1. All notifications, except the ones you unsubscribe from
  2. Important notifications about you or activity
  3. Only notifications about your account, security and privacy
2. LIVE VIDEO SETTINGS
  1. Turn off email notifications about comments added to your live video conversations
  2. Turn on email notifications about comments added to our live video conversations
3. OFFER SETTINGS
4. Turn off email notifications about offers you have saved
5. Turn on email notifications about offers you have saved
6. NOTIFICATIONS YOU HAVE TURNED OFF
  1. This list can be none to many, depending on what you have turned off. (Example list)
    1. Posts on your timeline
    2. Event cancellations
    3. Comments after you on a photo album
    4. Tags of your photos
    5. Mobile phone numbers shared with you
    6. Friend confirmations
    7. Requests for your mobile phone number
    8. Likes on your posts
    9. Tags of your videos
    10. Friend suggestions
    11. Friends added based on your suggestions
    12. comments on stories on your timeline
    13. comments after you on timeline stories
    14. Group name or description changes
    15. Photos uploads via email
    16. People you invited who join Facebook
    17. comments on posts you're tagged in
    18. Events you're invited to
    19. Posts from Close Friends
    20. Groups you're added to
    21. Posts from Close Friends
    22. Comments on your posts to groups
    23. Friends' timelines you're tagged on
    24. Posts to your groups
    25. Updates to an event you've joined
    26. Posts to events you've joined
    27. New followers of your lists
Desktop and Mobile

Desktop
1. See your notifications in the corner of your computer screen, even when Facebook is closed
Mobile
1. NOTIFICATIONS YOU'VE TURNED OFF (EXAMPLE LIST)
  1. Posts on your timeline
  2. Tags of your photos
  3. Friend confirmations
  4. Likes on your posts
  5. Tags of your videos
  6. comments on stories on your timeline
  7. Comments after you on timeline stories
  8. Comments on posts you're tagged in
  9. Events you're invited to
  10. Posts from Close Friends
  11. comments on your posts to groups
  12. Friends' timelines you're tagged on
  13. Updates to an event you've joined
  14. Posts you're tagged with
  15. Posts to events you've joined
  16. Friend requests
  17. Photos you've tagged in
  18. Comments on your photos
  19. Comments after you on a photo
  20. Comments on photos of you
  21. Upcoming birthdays
  22. You being tagged in a video
  23. Comments on your videos
  24. Replies to your comment on a video
  25. Approvals of requests to join groups
  26. Requests from friends through apps
  27. Likes on posts you're tagged in
  28. Reactions on posts you're tagged in
  29. Invitations to try apps
  30. You started broadcasting a live game from 3rd party app.
  31. Facebook Live bookmark

Other Notification settings are