  We calculate the resistance between two arbitrary grid points of several
infinite lattice structures of resistors by using lattice Green's functions.
The resistance for $d$ dimensional hypercubic, rectangular, triangular and
honeycomb lattices of resistors is discussed in detail. We give recurrence
formulas for the resistance between arbitrary lattice points of the square
lattice. For large separation between nodes we calculate the asymptotic form of
the resistance for a square lattice and the finite limiting value of the
resistance for a simple cubic lattice. We point out the relation between the
resistance of the lattice and the van Hove singularity of the tight-binding
Hamiltonian. Our Green's function method can be applied in a straightforward
manner to other types of lattice structures and can be useful didactically for
introducing many concepts used in condensed matter physics.
