英语作文写信的开头可以根据情境和关系的亲疏进行选择，以下是一些常见且实用的开头方式：

正式场合

Dear Mr./Ms. [Last Name], I hope this letter finds you in good health and high spirits. [亲爱的[姓氏]先生/女士，希望您一切安好。]

非正式场合

Hey [First Name]! It’s been a while since we last spoke. I hope you’re doing well! [嘿，[名字]!好久不见，希望你一切都好!]

表达感谢或询问

I am writing to express my gratitude for the opportunity to attend your presentation on global warming last week. [我写这封信是为了感谢您上周给我参加关于全球变暖演讲的机会。]

I am writing to inquire about the possibility of interning with your company. [我写这封信是想询问贵公司实习的可能性。]

表达关心

How is everything？ [近况如何？]

I hope you are doing well. [希望你一切顺利。]

引入主题

I have been thinking about... [我一直在考虑...]

It has been quite some time since we last communicated, so I want to take this opportunity to discuss about... [我们已经很久没有联系了，所以我想借此机会讨论...]

过渡语

I am writing to inform you of... [我想通知您...]

I am writing to say that... [我想说...]

I am writing to request more information about... [我想了解更多关于...]

期待回复

I am looking forward to receiving your letter. [我期待着您的来信。]

Please write to me as soon as possible. [请尽快回信。]

根据具体的写信目的和收信人关系，可以选择以上合适的方式进行开头，使信件显得既礼貌又自然。