I am trying to understand sphere packing problems, and it seems well-known that lattices can be only of certain kinds: the classical types (e.g. $A_n, B_n$, etc.) or the exceptional types (e.g. $E_8$).
Where can I find these lattices explained? Do they arise naturally?
(Note that I know nothing about lattices, but I heard they appear as root systems of Lie groups, or something of this kind)