Writing a thesis proposal I graduated last year and had been working on a problem. Now I have some progress and am interested in applying (non US places mostly, mathematical physics). How should I write a thesis proposal? I have the draft version of my work but it is extremely technical and will require serious patience to read the whole thing. Whoever I can summarize the important ideas in a smaller thing. 

My question is if I should attach an abstract, a summary and the draft of the paper along with the introductory mail? How should the mail be structured?

On a side note, one of the people at the institute had commended my work some time back when I had sent them a previous draft.
What worked for me was to select a potential advisor and schedule a meeting to check her interest on my ideas. Then I wrote that more or less like a project for technical people (that could come from different backgrounds, but in my field) structuring the text in a way that guided the reader.

Now, thinking back, it could have been easier to do it if I have structured it similar to a position paper.