This paper proposes a novel three-dimensional (3D) near-field beamforming (BF) design for Large Intelligent Surfaces (LIS). The key contributions include: (1) defining the Fresnel near-field region where phase variations are significant but amplitude variations are negligible, and showing that this region can be enlarged by a factor of four when considering imperfections in conventional 2D far-field BF. (2) Decomposing the optimal 3D-BF into a 2D far-field BF and a 1D near-field BF, which reduces codebook size and is compatible with existing 5G-NR systems. (3) Analyzing an optimal codebook design for the 1D near-field BF, showing that a small codebook can perform close to optimal. Numerical results demonstrate that the proposed 2D+1D BF design effectively recovers array-gains in the near-field of LIS. The paper also discusses the distinction between near-field and far-field regions of LIS, and how the near-field can be enlarged when the UE is slightly off the boresight. The decomposition theorem shows that 3D-BF in the Fresnel region can be designed in a simpler form. The paper concludes with a practical codebook design for 1D near-field BF, using the Lloyd-Max algorithm to optimize quantization and boundary points. The results show that the proposed 2D+1D BF design significantly reduces array-gain losses in the near-field of LIS.This paper proposes a novel three-dimensional (3D) near-field beamforming (BF) design for Large Intelligent Surfaces (LIS). The key contributions include: (1) defining the Fresnel near-field region where phase variations are significant but amplitude variations are negligible, and showing that this region can be enlarged by a factor of four when considering imperfections in conventional 2D far-field BF. (2) Decomposing the optimal 3D-BF into a 2D far-field BF and a 1D near-field BF, which reduces codebook size and is compatible with existing 5G-NR systems. (3) Analyzing an optimal codebook design for the 1D near-field BF, showing that a small codebook can perform close to optimal. Numerical results demonstrate that the proposed 2D+1D BF design effectively recovers array-gains in the near-field of LIS. The paper also discusses the distinction between near-field and far-field regions of LIS, and how the near-field can be enlarged when the UE is slightly off the boresight. The decomposition theorem shows that 3D-BF in the Fresnel region can be designed in a simpler form. The paper concludes with a practical codebook design for 1D near-field BF, using the Lloyd-Max algorithm to optimize quantization and boundary points. The results show that the proposed 2D+1D BF design significantly reduces array-gain losses in the near-field of LIS.