TITLE: Where can I find details of Elie Cartan's thesis?
QUESTION [12 upvotes]: I am interested in the details of Elie Cartan's thesis, and, more specifically the explicit construction of the exceptional Lie groups as groups of symmetries of some specific homogeneous polynomials (according to what I have read in many places). I am interested in the details. For instance, what does one such a polynomial look like? What do all such polynomials (with groups of symmetry a fixed exceptional Lie group) look like? Is the set of all such polynomials dense in the relevant polynomial space? 
Also, I am interested in different realizations of the exceptional Lie groups: for instance, $G_2$ is the group of symmetries of a skew-symmetric trilinear form on $\mathbb{C}^7$. And in this case, the space of such skew-symmetric trilinear forms is dense in the set of all skew-symmetric trilinear forms on $\mathbb{C}^7$.
So I guess in general, I am interested in concrete and explicit realizations of the exceptional Lie groups as groups of symmetries of a specific algebraic object. Also what is the set of all such objects with this property? And, is the set of all such objects dense in the relevant vector space? I hope my questions are sufficiently clear!

REPLY [3 votes]: All details about Cartan's thesis can be found in the thesis itself:
https://archive.org/details/surlastructured00bourgoog
There is also a German translation for those who do not read French:
Ueber die einfachen Transformationsgruppen. (German) JFM 25.0638.01
Leipz. Ber. XLV. 395-420 (1893).