  The famous Rogers-Ramanujan and Andrews--Gordon identities are embedded in a
doubly-infinite family of Rogers-Ramanujan-type identities labelled by positive
integers m and n. For fixed m and n the product side corresponds to a
specialised character of the affine Kac-Moody algebra A_{2n}^{(2)} at level m,
and is expressed as a product of n^2 theta functions of modulus 2m+2n+1, or by
level-rank duality, as a product of m^2 theta functions. Rogers-Ramanujan-type
identities for even moduli, corresponding to the affine Lie algebras C_n^{(1)}
and D_{n+1}^{(2)}, are also proven.
