This article, published in 1962 as Chapter 7 of *Gravitation: an introduction to current research*, presents a novel formulation of General Relativity by Arnowitt, Deser, and Misner. The authors aim to clarify the dynamics of the gravitational field by separating the true dynamical variables from those that merely describe the coordinate system. They argue that the coordinate invariance of general relativity is analogous to the gauge invariance in electromagnetism, leading to difficulties in identifying the independent dynamical modes. To address this, they employ techniques from Lorentz covariant field theories, such as those developed by Schwinger, to disentangle the gauge from the dynamical variables. The authors show that the theory can be cast into a canonical form, involving only the minimal number of variables needed to describe the system. This form is essential for quantization, as it allows for the direct computation of Poisson brackets among the canonical variables. The canonical formalism also enables the identification of the independent excitations of the gravitational field, which are crucial for defining gravitational radiation in a coordinate-independent manner. The article discusses the use of the Palatini Lagrangian and a 3+1 dimensional decomposition of the spacetime metric. This approach allows the theory to be expressed in a form that is invariant under arbitrary coordinate transformations, similar to parameterized mechanics. The authors then show that the gravitational field equations can be reduced to a canonical form, with the Hamiltonian defined in terms of the canonical variables. The Hamiltonian provides a definition of total energy and momentum, which are invariant under certain coordinate transformations. The analysis is extended to include the coupling of other systems to the gravitational field, leading to a discussion of self-energy questions. The authors demonstrate that the canonical formalism is essential for recognizing pure particle states and for defining the total mass of a classical electron in terms of its charge. The results are contrasted with perturbation analyses, which often lead to divergences. The article concludes with a discussion of the implications of the canonical formalism for the quantization of general relativity. While the classical formulation provides a clear path to quantization, the non-linear nature of the theory may require more subtle methods. The authors also speculate on the role of the canonical formalism in quantum gravity, noting that the results obtained in classical theory may provide insights into the quantum regime.This article, published in 1962 as Chapter 7 of *Gravitation: an introduction to current research*, presents a novel formulation of General Relativity by Arnowitt, Deser, and Misner. The authors aim to clarify the dynamics of the gravitational field by separating the true dynamical variables from those that merely describe the coordinate system. They argue that the coordinate invariance of general relativity is analogous to the gauge invariance in electromagnetism, leading to difficulties in identifying the independent dynamical modes. To address this, they employ techniques from Lorentz covariant field theories, such as those developed by Schwinger, to disentangle the gauge from the dynamical variables. The authors show that the theory can be cast into a canonical form, involving only the minimal number of variables needed to describe the system. This form is essential for quantization, as it allows for the direct computation of Poisson brackets among the canonical variables. The canonical formalism also enables the identification of the independent excitations of the gravitational field, which are crucial for defining gravitational radiation in a coordinate-independent manner. The article discusses the use of the Palatini Lagrangian and a 3+1 dimensional decomposition of the spacetime metric. This approach allows the theory to be expressed in a form that is invariant under arbitrary coordinate transformations, similar to parameterized mechanics. The authors then show that the gravitational field equations can be reduced to a canonical form, with the Hamiltonian defined in terms of the canonical variables. The Hamiltonian provides a definition of total energy and momentum, which are invariant under certain coordinate transformations. The analysis is extended to include the coupling of other systems to the gravitational field, leading to a discussion of self-energy questions. The authors demonstrate that the canonical formalism is essential for recognizing pure particle states and for defining the total mass of a classical electron in terms of its charge. The results are contrasted with perturbation analyses, which often lead to divergences. The article concludes with a discussion of the implications of the canonical formalism for the quantization of general relativity. While the classical formulation provides a clear path to quantization, the non-linear nature of the theory may require more subtle methods. The authors also speculate on the role of the canonical formalism in quantum gravity, noting that the results obtained in classical theory may provide insights into the quantum regime.