Formal 

opening statements

1. I am writing this letter with regards to the scholarship program to study at London University which I read in Sunday Times on December 1st, 2014. 

2. I am writing in connection with my recent stay at the Four Seasons in London, England. Due to a malfunctioning heater in my room, I spent three miserable nights at your hotel from April 26-29, 2010. 

3. I am writing to complain about ...

4. I am writing in response to ...

5. I am writing to express my dissatisfaction with  ...

6. I am writing to express my gratitude for ... 

closing statements 

1. I would like to thank you in advance for .. 

2. Thank you for giving your attention to this complaint/matter.

3. I look forward to your reply. 

4. I would be grateful if you could/would ... 

Semi-Formal  

opening statements

1. I'm just writing to say thank you for the offer of joining your company.

closing statements 

1. I would be very grateful if you could allow me to take these four days off as it is very important to my parents. 

Informal/Personal  

opening statements

1.  It's been so long since we last were in touch but I haven't forgotten all the wonderful times we spent together last year. It's my birthday coming up and I want to invite you over to stay at my place for the celebration. 

2. I just thought I'd like o let you know that I finally quit my job ...

3. I'm writing to tell you about  .......

4. I thought you might be interested to know/hear that ......

5. I thought you would like to hear about .......

closing statements 

1. I can't wait to hear all about ...

2. Write back soon with your news 

3. Let me know if you need  .../want ... / are able to visit ... 

4. I'm looking forward to hearing al about ...