The paper by William Gordon Ritter reviews the concept of geometric quantization, which aims to bridge the gap between classical and quantum mechanics by defining a mathematical framework for observables. The author begins by discussing the relationship between classical and quantum observables, highlighting the Heisenberg picture in quantum mechanics and the Poisson bracket in classical mechanics. The core of the paper is the introduction of geometric quantization, which involves prequantization and the quantization process itself. Prequantization is described as a method to construct a quantum mechanical Hilbert space from a classical symplectic manifold. This process involves the use of a prequantum bundle and a polarization, which helps in defining a bijective correspondence between classical observables and quantum operators. The paper also discusses the irreducibility postulate, which ensures that the Hilbert space is irreducible under the action of the quantum observables. The quantization process is detailed, focusing on the construction of a Hilbert space from sections of a prequantum bundle that are covariantly constant along a chosen polarization. The paper introduces the concept of a Lagrangian distribution and admissible polarizations, which are essential for the quantization procedure. It also explains how to define a scalar product on the space of sections of the prequantum bundle, leading to the correct modification of the Bohr-Sommerfeld conditions. Finally, the paper discusses the quantization of observables and the relationship between different representations of the cotangent bundle, such as the Schrödinger and momentum representations. The paper concludes with references to classical and quantum mechanics literature.The paper by William Gordon Ritter reviews the concept of geometric quantization, which aims to bridge the gap between classical and quantum mechanics by defining a mathematical framework for observables. The author begins by discussing the relationship between classical and quantum observables, highlighting the Heisenberg picture in quantum mechanics and the Poisson bracket in classical mechanics. The core of the paper is the introduction of geometric quantization, which involves prequantization and the quantization process itself. Prequantization is described as a method to construct a quantum mechanical Hilbert space from a classical symplectic manifold. This process involves the use of a prequantum bundle and a polarization, which helps in defining a bijective correspondence between classical observables and quantum operators. The paper also discusses the irreducibility postulate, which ensures that the Hilbert space is irreducible under the action of the quantum observables. The quantization process is detailed, focusing on the construction of a Hilbert space from sections of a prequantum bundle that are covariantly constant along a chosen polarization. The paper introduces the concept of a Lagrangian distribution and admissible polarizations, which are essential for the quantization procedure. It also explains how to define a scalar product on the space of sections of the prequantum bundle, leading to the correct modification of the Bohr-Sommerfeld conditions. Finally, the paper discusses the quantization of observables and the relationship between different representations of the cotangent bundle, such as the Schrödinger and momentum representations. The paper concludes with references to classical and quantum mechanics literature.