This paper presents a theory for calculating all-electron NMR chemical shifts using pseudopotentials, applicable to both finite and infinitely periodic systems. The theory is based on an extension of the Projector Augmented Wave (PAW) method, known as the Gauge Including Projector Augmented-Wave (GIPAW) approach. The GIPAW method ensures translational invariance in the presence of a magnetic field, which is crucial for accurate calculations of magnetic properties. The theory is validated against quantum chemical results for molecules and against all-electron plane-wave calculations for diamond. The GIPAW method allows for the calculation of NMR chemical shifts in solid-state systems, overcoming previous limitations of pseudopotential approximations. The method is implemented in a plane-wave pseudopotential electronic structure code, and the results are compared with other approaches, including the MPL method and the single gauge method. The paper also discusses the importance of gauge invariance and the role of the generalized f-sum rule in ensuring the consistency of different approaches to calculating NMR chemical shifts. The GIPAW method is shown to be computationally efficient and accurate, providing a reliable framework for the calculation of magnetic properties in solid-state systems.This paper presents a theory for calculating all-electron NMR chemical shifts using pseudopotentials, applicable to both finite and infinitely periodic systems. The theory is based on an extension of the Projector Augmented Wave (PAW) method, known as the Gauge Including Projector Augmented-Wave (GIPAW) approach. The GIPAW method ensures translational invariance in the presence of a magnetic field, which is crucial for accurate calculations of magnetic properties. The theory is validated against quantum chemical results for molecules and against all-electron plane-wave calculations for diamond. The GIPAW method allows for the calculation of NMR chemical shifts in solid-state systems, overcoming previous limitations of pseudopotential approximations. The method is implemented in a plane-wave pseudopotential electronic structure code, and the results are compared with other approaches, including the MPL method and the single gauge method. The paper also discusses the importance of gauge invariance and the role of the generalized f-sum rule in ensuring the consistency of different approaches to calculating NMR chemical shifts. The GIPAW method is shown to be computationally efficient and accurate, providing a reliable framework for the calculation of magnetic properties in solid-state systems.