>>Ever since I installed Outlook 365 and whenever I open it, I get a message Internet Security Warning (see msg 1 attached).
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>>When I click on View button I get the Certificate window (see msg 2 attached)
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>>I click on Install Certificate go through the Installation steps.
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>>But then, on the next opening of Outlook, I get the same message of the Certificate.
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>>Is this certificate related to AV (Avast) or my email?
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>I am also getting that. I assume you have configured your account to use authentication for SMTP. Is that correct? This is what I have and had this a few times. Basically, even if you install, it will remove that procedure and re-ask the next times you will enter that software. Then, after a while, it will go away. This seems to act exactly like the SSL EV certificate on IE which reacts exactly the same.

First, thank you. Do I understand then, that this message about Internet Certificate is benign and I should not worry about it?

I wonder why when I was using Outlook 2010 (on my old computer) I never had this message about Internet Certificate. I will check my old computer (where Outlook 2010 is installed) to see how email account is configured.