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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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Easiest way to distinguish $E_8 \oplus E_8$ from $E_{16}$
In sage, you can use the command .is_globally_equivalent_to(), which allows you to compare two quadratic forms. See the Quadratic Forms Overview.