1) The first paragraph is concise, briefly introducing who I am and explaining my purpose.
2) The second paragraph briefly introduces what school you are in, what major you are studying, what your grades are, and what scientific research projects you have done.
3) The third paragraph briefly talks about your understanding of the professor (I think you are excellent in a certain field. I have read your paper, and the XXX method (or result) in it makes me feel very interested. I really hope to study in your laboratory at XX time. Please give me a chance, which will be very helpful to my academic development.
4) In the fourth paragraph, I once again asked for an opportunity to explain. I attached my resume for the professor to see and thank him.