"Mam" is not a word in English. The word you are thinking of is "Ma'am," which is short for "Madam." In the U.S. we use "Ma'am" primarily in speech. When you are talking to a lady, it is polite to use "Ma'am," especially in the South of the U.S.
In writing a letter, "Madam" is formal and polite. If you are writing to a woman who is in an official position (e.g., a government official), you could start a letter with "Dear Madam." If you are writing to someone in a professional position and you are not sure if it is a man or a woman, you can say "Dear Sir or Madam." If you are addressing a group of people, the salutation is:
Ladies:
Gentlemen:
Ladies and/or Gentlemen:
(The word "Dear" is dropped.)
What is the proper salutation for a register of wills, e.g. Honorable John White?
the correct salutation for two men is Messrs
Hello.
Your Honor
Dean actually is the proper salutation. One could say: Dean Redmond, would you please sign this form? Alternatively you could just use the Dr. salutation or the Professor salutation if those are appropriate, which they generally are.
The proper salutation for a doctor is doctor or professor depending on their title. In writing the short form can be used which will be Dr. or Prof.
A proper salutation for greeting the president of a business is "Dear Mr. President". To conclude a letter, the proper word is "Sincerely" and a the name of the writer.
miss
Miz.
His/Her Excellency
A dentist can either have a Doctorate of Dental Medicine (DMD) or Doctorate of Dental Surgery (DDS). The proper salutation for a dentist is Doctor.
His honor or Your honor is the proper salutation for a retired judge. The use of the word judge in title and introductions is not used after retirement.