Invasion of Privacy?

Is it an invasion of privacy to e-mail someone with out their permission by using their e-mail address cut from a forwarded e-mail sent to you from a mutual aquaintence?

Yes it is! The first faux pas here is that whomever sent that forwarded e-mail should have put all their contact's e-mail addresses in the Bcc: field rather than expose all those e-mail addresses to strangers. By doing so they were the first to invade the privacy of their contacts by publicly displaying their e-mail addresses.

It would depend on what you are e-mailing them about and what you mean by mutual acquaintance. If you met this person that is one thing. If you the only thing you have in common is that you both know the sender but not each other, it is not recommended. Understand the issue here is you have an e-mail address that was not provided to you by its owner and you need to govern yourself accordingly when thinking of using it.

If you are e-mailing about something you can commercially gain from you definitely should not e-mail this "acquaintance." If it is about something personal, then I would start the e-mail with an reminder greeting about how/when you met and a "hope you don't mind if I e-mail you..." type of statement.

That said, don't be surprised if they don't appreciate getting an e-mail from a stranger regardless of who you both know in common. I have an article on my site about the E-mail Etiquette involved in using the Bcc: field for your reading pleasure.