You might want to clarify your post. Do you mean that you can only view your @gmail account on the web and not in mail, or do you mean that your mail is not going to your apple address (@icloud, or @me) account.
If you want to view your gmail in the mail app, the setup is straight forward. If you use 2 step verification, you have to create an app password in gmail and use that instead of your log in password. Click on your gmail address in the top right and go to account, and then security. If 2 step verification is on, go to app password settings and generate on for your mail app. Just copy and paste that password into your Mail app.
If it's the latter, when you signed up for gmail; you may have turned on mail forwarding; again this is simple to change. Go to settings, and then accounts. If your other account is listed, just delete it as it's forwarding your mail to your gmail account.
Thank you for that. It is the first, ie I can only view my e-mail on the web. But I can't follow your solution. You say to click on my e-mail address in the top right. The top right of what? If I open Mail, there is no e-mail address on the top right. I have looked at Mail in settings, but that does not seem to be to what you are referring.
I was referring to the top right of the gmail web browser. From the sound of the problem you have 2 step enabled, and your gmail password will not work in the Mail app with that enabled. Your 2 options are to disable 2 step (wouldn't recommend for security reasons), or to go into your security settings in the gmail web app to create an app specific password.
Delete gmail account. Turn on Mail on iCloud. Register for email address from iCloud.
Thank you. That proved to be a simple and effective solution. Problem solved. I am now back on Mail. Well done.
No, I am not out of the woods yet. I am doing this on my wife's mac using OS10.7.5. Now using only iCloud, I am unable to insert the incoming mail server. It is greyed and won't allow me to insert anything. So Mail will send e-mails but does not receive any. Ideas?