I ... could not add my Google based account

You didn't tell what prevents you from adding the account.

I ... could not add my Google based account

You didn't tell what prevents you from adding the account.

It just says: "Login to account ____@drept.unibuc.ro failed Login to server drept.unibuc.ro with username _____ failed."

I have also looked in the account settings and both POP and IMAP are activated.

And I have also tried adding the Google based account on Thunderbird using both IMAP and POP. It still doesn't work.

What server settings are you using when trying to set up the account? For Google make sure to use 'OAuth2' as 'Authentication method'.

I just selected set up an account->email, inserted my name, email address and password, then left it to IMAp, as it was selected, as I did with the first Gmail account that worked.

I did not select manual config or other advanced settings... to be honest, I do not have any idea where the 'Authentication method' option is.

I hope this is clear enough... I also have the error: Unable to log in at server. Probably wrong configuration, username or password.

In your 3rd picture, don't click Done, click Manual config. and enter the correct gmail settings: incoming IMAP server imap.gmail.com on 993, SSL/TLS, OAuth2 authentication, User name = your unibuc.ro address; outgoing SMTP server smtp.gmail.com on 587, STARTTLS, (or 465 SSL/TLS), OAuth2 authentication, User name = your unibuc.ro address. If OAuth2 isn't visible in the authentication menu, click Advanced config. in the Manual config. window and set the authentication there.

Before doing this, make sure IMAP is enabled in your mail settings when viewed in webmail.

Great, thanks a lot!