Word choice for salutation in a formal email to your PhD adviser, Is *Dear Boss* appropriate? I am a first year PhD student in France, born and raised in India. It is not customary in here where I am doing my PhD to call one's adviser boss but I do, partly due to my reluctance to call her by the first name, partly attributed to the culture in which I am brought up. As one comment suggested, "Dear professor" would have been an appropriate choice but she doesn't have any teaching duties and is a full time researcher. I would have used "Dear Madam" if I were in India but no one here use that. I think "Dear Dr. X" is too formal and no one here use that either. Many prefer "Hi X" but I think that is too informal. 
Now that I am writing an email, Is Dear Boss an appropriate salutation? If not, what would be an appropriate salutation in a formal email?
In my view, in academia, the word "Boss" carries a large amount of semantic baggage that you probably don't want to invoke. Although you mean it to be polite and respectful, it also has an ironic context which you may not have detected. By saying "Dear Boss" can also imply that in your opinion they are neither dear to you or deserve the respect as a superior. It is safest to avoid such salutations altogether in emails.

As others have indicated this is very culturally dependent and I think you are bringing too much of your south asian culture to a european environment. Do what the locals do and emulate other peers is the safest and wisest approach.