Based on Purpose:
1. Personal Letter: A letter written to a specific person, often expressing personal thoughts, feelings, or news.
2. Business Letter: A formal letter used for professional communication, such as job applications, inquiries, or complaints.
3. Formal Letter: A letter written in a formal tone and style, often used for official correspondence or invitations.
4. Informal Letter: A letter written in a relaxed and conversational style, often to friends or family.
5. Cover Letter: A letter accompanying a resume or other application materials, explaining the applicant's qualifications and interest in the position.
6. Complaint Letter: A letter written to express dissatisfaction with a product, service, or situation.
7. Thank You Letter: A letter expressing gratitude for a gift, service, or kindness.
Based on Format:
1. Block Letter: A letter format where all text is aligned to the left margin.
2. Modified Block Letter: A letter format where the date, closing, and signature are aligned to the right margin.
3. Semi-Block Letter: A letter format where the date, closing, and signature are indented, while the body paragraphs are aligned to the left margin.
4. Full Block Letter: A letter format where all text, including the date, closing, and signature, is aligned to the left margin.
5. Hanging Indent Letter: A letter format where the first line of each paragraph is aligned to the left margin, while the subsequent lines are indented.
6. Open Punctuation Letter: A letter format that does not use punctuation marks after the salutation or closing.
7. Mixed Punctuation Letter: A letter format that uses punctuation marks after the salutation and closing.
Based on Delivery:
1. Handwritten Letter: A letter written by hand.
2. Typed Letter: A letter written using a typewriter or computer.
3. Email Letter: A letter sent electronically through email.
4. Fax Letter: A letter sent electronically through a fax machine.
5. Snail Mail Letter: A letter sent through the postal service.
Ultimately, the "kinds of letters" depends on the context of your question. It's helpful to be more specific about what you're looking for!