Email to potential PhD supervisor I am a PhD applicant and I am preparing to send an introductory email to a potential supervisor.

I have two questions:


I am self-funded. Should I mention this in the initial email?
Is the following sentence grammatically correct?



  I would be delighted to undertake a research project under your supervision, kindly let me know if this might be a possibility; I have attached my CV and academic transcript for your consideration.
You could mention self funding or not. However, it is important that you give some indication of why you are interested in this person and what it is in your background that might interest him/her in you. Mentioning past research projects in the same specialty would be helpful. Your statement is fine, but only as an opening. 

In particular, you should investigate the background of the potential supervisor, including publications and past students. In mathematics, for example, the Genealogy project can give you information about where the person fits - advisor and students. For famous people, even wikipedia will give you information.