  The properties of antiferromagnetic Heisenberg $S=\frac{1}{2}$ ladders with
2, 3, and 4 chains are expanded in the ratio of the intra- and interchain
coupling constants. A simple mapping procedure is introduced to relate the 4
and 2-chain ladders which holds down to moderate values of the expansion
parameters. A second order calculation of the spin gap to the lowest triplet
excitation in the 2- and 4-chain ladders is found to be quite accurate even at
the isotropic point where the couplings are equal. Similar expansions and
mapping procedures are presented for the 3-chain ladders which are in the same
universality class as single chains.
