The U-Net architecture has transformed image segmentation. U-Net’s versatility and accuracy have driven its widespread adoption, significantly advancing fields reliant on machine learning problems with images. In this work, we give a clear and concise mathematical ex- planation of Unet. We explain what is the meaning and function of each of the components of Unet. We will show that Unet is solving a control problem. We decompose the control variables using multigrid methods. Then, operator-splitting techniques is used to solve the problem, whose architecture exactly recovers the UNet architecture. Connections between the proposed algorithm and general networks are also discussed. Our result shows that UNet is a one-step operator-splitting algorithm for the control problem. This talk is based on joint works with: Liu Hao, Raymond chan and Lingfeng Li.