Coding schemes for the binary memorylessT-user adder channel are investigated in this paper. First upper and lower bounds on the capacity sum, which are asymptotically tight with increasingT, are derived for the noiseless case. Second, a class ofT-user uniquely decodable codes with rates, asymptotically inT, equal to the maximal achievable values is constructed. A decoding algorithm for these codes is also presented. Next, a class of error-correcting codes for the noisyT-user adder channel is constructed. It is shown that these codes can he used to construct multilevel codes suitable for use on the additive white Gaussian noise channel.