This is a revised description and manual for the primordial nucleosynthesis program, NUC123, an updated and modified version of the code of R.V. Wagoner. NUC123 has undergone a number of changes, further enhancing its documentation and ease of use. Presented here is a guide to its use, followed by a series of appendices containing specific details such as a summary of the basic structure of the program, a description of the computational algorithm, and a presentation of the theory incorporated into the program.