Mail app on MacBook Air not receiving emails from Gmail, Yahoo, or Outlook

I have issues with the Mail App; every once in a while, it says the server is offline, like Gmail, Yahoo, or Outlook, and I don't receive any emails from the service provider. However, I do get emails when I visit the source website. I want to see all my mail in one place so it's easier for me to manage my emails.

[Re-Titled by Moderator]

Original Title: Mail on MacBook Air