After we announce our projects for the term, we get many emails from students. Some write too short (“I am interested in your project”), others too long(their whole career plan in a page, ending with some specific question or request somewhere in the mail). They both sit in the inbox waiting to be answered (what to write, what info to ask,…).. Also, do not assume the prof has only one project (so dont say “I am interested in your project”).
Instead, you should read up/think as much about the project as you can, commit on time (they fill quickly), give relevant info about yourself especially citing related coursework and why you would like to be in that project… and then, ask me to consider you to the project. Another thing to keep in mind is that project work is like apprenticeship, so it is often difficult for profs to take extra students.