該雜志發表了簡短的通訊、研究和評論文章，致力于幾何方法(包括交換和非交換微分幾何、黎曼幾何、芬斯勒幾何、復幾何、李群和李代數、束理論、同調和上同調、代數幾何、全局分析、范疇理論、算子代數和拓撲)在數學和理論物理的所有領域的所有應用，包括:經典力學(拉格朗日、哈密頓、泊松公式);量子力學(也是半經典近似);ODE和PDE的哈密頓系統及其可積性物理變分結構與守恒定律系統與連續體熱力學(亦稱量子熱力學與統計物理學);廣義相對論和其他幾何引力理論;粒子物理學的幾何模型;超重力與超對稱場理論經典場論和量子場論(亦稱彎曲背景下的量子化);計理論;拓撲領域理論;弦、膜和擴展對象理論;全息術;量子引力、環量子引力和量子宇宙學;量子群的應用;量子計算;控制理論;幾何的混亂。

This journal publishes short communications, research and review articles devoted to all applications of geometric methods (including commutative and non-commutative Differential Geometry, Riemannian Geometry, Finsler Geometry, Complex Geometry, Lie Groups and Lie Algebras, Bundle Theory, Homology an Cohomology, Algebraic Geometry, Global Analysis, Category Theory, Operator Algebra and Topology) in all fields of Mathematical and Theoretical Physics, including in particular: Classical Mechanics (Lagrangian, Hamiltonian, Poisson formulations); Quantum Mechanics (also semi-classical approximations); Hamiltonian Systems of ODE's and PDE's and Integrability; Variational Structures of Physics and Conservation Laws; Thermodynamics of Systems and Continua (also Quantum Thermodynamics and Statistical Physics); General Relativity and other Geometric Theories of Gravitation; geometric models for Particle Physics; Supergravity and Supersymmetric Field Theories; Classical and Quantum Field Theory (also quantization over curved backgrounds); Gauge Theories; Topological Field Theories; Strings, Branes and Extended Objects Theory; Holography; Quantum Gravity, Loop Quantum Gravity and Quantum Cosmology; applications of Quantum Groups; Quantum Computation; Control Theory; Geometry of Chaos.