This is a brief recommendation how to write emails in academic and school environment. It expresses my personal opinion, based on several years of experience in writing and reading emails. You may browse internet to see other recommendations to get more diverse opinions.
I am always happy if I get email from you, and I don't mind the format, misssstypes or mistakes. Take the following advice as a practice for future - eventually, once you will need to write an English email to some of your advisors, colleagues, or researcher with whom you are going to have some cooperation. Let's use our email communication as a practice of good habits in writing formal English emails.
Important note at the beginning: email is not a Facebook message. It has a stable structure, with the salutation, email body, signing off and signature. You don't need to be that formal if you just reply to another email and the reply is short, but it's always better to be a little more formal at the beginning of conversation to make a positive impression.
Note: before you write to a person, make sure what is her/his given name (first name) and what is the surname (family name, last name). This may not always be obvious. My first name is David and surname is Zeleny, written as David Zeleny (first name comes first). In Taiwan, especially if written in Chinese, names starts usually by surname - like Li, Lin, Chen, Wang etc., followed up by given name (like Hsin-Han, Chang-Fu etc.), often written as Surname, Given-Name (e.g. Hsieh, Chang-Fu). To make the distinction between the given name and the surname is important!
If you are not sure whether you should start with super-formal salutation or use some more friendly or familiar way, there is one unwritten rule: in the first email to the person you don't know well, it is always better to be formal. If the conversation continues and you will write that person another email, check the way how the person signed off. If they used their first name as signature (e.g. Cheers, David), in the next email you may start with more familiar salutation (e.g. Dear David). But if the first response email ended up formally (e.g. Best regards, Zeleny), than it's better to keep using the formal salutation even in the follow-up emails. Don't expect that everybody will directly offer you friendly way of communication - some people, especially if they are teachers and communicate with their students, prefer to keep formal distance.
It's always good to put the greetings at the end of the email on extra line. The following are sorted from the most to the least formal:
After the greetings at the end, don't forget to ALWAYS write your name (Chinese, English, nickname - depends what you prefer; in the first email to person you don't know, always use your whole name (without any title). In the follow up emails, when you became more familiar, to use just the first name is fine. If you have Chinese name, in English email it's better to use English transcription of Chinese characters (the one you get in your passport) instead of using directly Chinese characters - the person you are writing (e.g. me) may not be able to read Chinese, and then will have no idea how to pronounce your name (and probably won't even know who you are, even though you may meet frequently). If you have English nickname (like Jeff or Alvin, feel free to use it in the follow up emails, but in the first email always write your formal name (eventually with the nickname enclosed in parentheses after).
Example of email good for the first contact in academic environment:
Dear Dr. Zeleny,
I would like to request pdf of your recent publication in Science1).
Chen Ching-Feng (Alvin)
Example of email to somebody you are somewhat familiar:
Not sure how can I solve the exercise you gave us as homework assignment. I am not sure which function I should use for it. Could you give me a hint?
And the example of formally bad email:
Hello Prof. David!
Good day! I can't solve the homework, any help?
What's wrong? The use of title (Prof.) with first name instead of surname is a mistake. Starting the body of the email with another salutation (Good day!) is not necessary in an English email. Signing off using very informal Bye bye style, which is good if spoken, but not good if written, is also not a good idea. And - signature at the end is missing. It may not always be obvious who actually is the author of the email, especially if you use email address like email@example.com or firstname.lastname@example.org.
One simple rule - it is a good habit to always answer emails, if they are addressed directly to you, even if the email's author does not specifically request the answer. Also the other way around - if you ask a question or suggestion, and you get an email with response, it's always a good idea to ping back a short reply - something like “Thanks, this is usefull”, or “Ok, I will think about that”, or “I already solved that, but still appreciate your help” etc (this is basically an analogy of “like” or “thumbs up” on Facebook). This is to show that you actually got the email, you read it and it was of some use to you. Of course there are some healthy limitations - if the conversation lasts for a while and couple of emails are being exchanged, you don't need to specifically response to each of them in this way. Remember - it never looks bad if you respond email, but it may sometimes look bad if you do not.
You will find many similar advices on internet. I found particularly usefull the advice of Grammarly (a company which offers English proof reading tool). And if you need a cartoon summary of the suggestions above, you should definitely check PhD comics. Good luck with writing your emails!