This paper addresses the challenge of applying conventional multi-user MIMO precoding techniques in millimeter wave (mmWave) systems due to hardware constraints. It proposes a low-complexity hybrid analog/digital precoding algorithm for downlink multi-user mmWave systems, which combines analog and digital processing to reduce power consumption. The algorithm involves configuring hybrid precoders at the transmitter and analog combiners at multiple receivers with minimal training and feedback overhead. The performance of the proposed algorithm is analyzed in the large-dimensional regime and single-path channels, showing higher sum rates compared to analog-only beamforming solutions. The rate loss due to joint quantization is characterized, and the algorithm's performance is compared with analog-only beamforming solutions. Analytical and simulation results demonstrate that the proposed hybrid precoding algorithm achieves good performance with reduced training and feedback overhead, leveraging the sparse nature of mmWave channels and the large number of antennas.This paper addresses the challenge of applying conventional multi-user MIMO precoding techniques in millimeter wave (mmWave) systems due to hardware constraints. It proposes a low-complexity hybrid analog/digital precoding algorithm for downlink multi-user mmWave systems, which combines analog and digital processing to reduce power consumption. The algorithm involves configuring hybrid precoders at the transmitter and analog combiners at multiple receivers with minimal training and feedback overhead. The performance of the proposed algorithm is analyzed in the large-dimensional regime and single-path channels, showing higher sum rates compared to analog-only beamforming solutions. The rate loss due to joint quantization is characterized, and the algorithm's performance is compared with analog-only beamforming solutions. Analytical and simulation results demonstrate that the proposed hybrid precoding algorithm achieves good performance with reduced training and feedback overhead, leveraging the sparse nature of mmWave channels and the large number of antennas.