This paper presents a theory for the *ab initio* calculation of all-electron NMR chemical shifts in insulators using pseudopotentials. The theory is formulated for both finite and periodic systems and is based on an extension of the Projector Augmented Wave (PAW) approach by Blöchl and the method by Mauri *et al*. The theory is validated for molecules by comparing with quantum chemical results and for periodic systems by comparing with plane-wave all-electron results for diamond. The key innovation is the Gauge Including Projector Augmented-Wave (GIPAW) method, which ensures translational invariance in the presence of a magnetic field. The GIPAW Hamiltonian and current operator are derived, and the expressions for the current response in finite and periodic systems are presented. The GIPAW method is implemented in a plane-wave pseudopotential electronic structure code, and its practicality is demonstrated through the calculation of NMR chemical shifts. The paper discusses the computational aspects of the implementation, including the application of the Green function, the velocity operator, and the evaluation of limits in periodic systems.This paper presents a theory for the *ab initio* calculation of all-electron NMR chemical shifts in insulators using pseudopotentials. The theory is formulated for both finite and periodic systems and is based on an extension of the Projector Augmented Wave (PAW) approach by Blöchl and the method by Mauri *et al*. The theory is validated for molecules by comparing with quantum chemical results and for periodic systems by comparing with plane-wave all-electron results for diamond. The key innovation is the Gauge Including Projector Augmented-Wave (GIPAW) method, which ensures translational invariance in the presence of a magnetic field. The GIPAW Hamiltonian and current operator are derived, and the expressions for the current response in finite and periodic systems are presented. The GIPAW method is implemented in a plane-wave pseudopotential electronic structure code, and its practicality is demonstrated through the calculation of NMR chemical shifts. The paper discusses the computational aspects of the implementation, including the application of the Green function, the velocity operator, and the evaluation of limits in periodic systems.