How do I add a 2nd gmail account to my Mac?

I am not able to view emails from a second gmail account which I have. When I reinstall the second account, the message comes up that this account already exists. How do I get my mail to recognize it?

Mail > Mail menu > Accounts.

my mail contacts don't list my second gmail account. It was loaded in the computer but it isn't listed under. mail accounts. Any suggestions?

I need to list a second gmail address in my Mac Mail, both on my Mac Air and my Iphone Mac Mail. Will not allow the second gmail address Please help?