TITLE: Higher Composition Law
QUESTION [7 upvotes]: Prof M.Bhargava's work on "Higher Composition Law" which solved some outstanding conjectures on number theory seems to be very interesting topic. I have seen his papers but, in spite of the titles, it is not easy to understand (Of course in my point of view, for sure there are many people who can understand it easily). 
Do you know any lecture note or expository paper which explains more details and some explicit example? especially his work on composition law for binary quadratic form. 
Thanks

REPLY [9 votes]: I have lecture notes that I'd like to turn into a book one day. I have not yet had time to adapt to my new TeX system, and the drawings done via ps-tricks do not yet come out as planned. In addition, there are gaps and mistakes that I have not yet had time to fill and correct (the chapter on composition should be essentially correct and complete, however). In any case, the present set of notes, for the time being, can be found
here. Comments and
corrections are welcome.

REPLY [5 votes]: Try the Bourbaki talk given by Karim Belabas a couple of years ago :
Paramétrisation de structures algébriques et densité de discriminants [d'après Bhargava]
Astérisque, Vol. 299 (2005), Exp. No. 935, pp. 267-299, Séminaire Bourbaki. Vol. 2003/2004,MR 2167210.