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Algebraic and geometric theory of quadratic forms and symmetric bilinear forms, e.g., values attained by quadratic forms, isotropic subspaces, the Witt ring, invariants of quadratic forms, the discriminant and Clifford algebra of a quadratic form, Pfister forms, automorphisms of quadratic forms.
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Involution of $E_{8}$ lattice
As André already pointed out, it is sufficient to study the Weyl group $E_8$, looking in the atlas certainly works, see b).
a) BUT the Weyl group perspective makes it in my opinion enough accessible …