MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. MPAG currently has three sections: 1. Probability and Statistical Physics, 2. Quantum Theory and 3. Integrable Systems. Authors wishing to submit articles from other areas of mathematical physics, in particular geometry, must demonstrate the connection of their research with the aims and scope of one of these sections. The section on Probability and Statistical Physics focuses on applied probability problems with a particular interest in probabilistic models and stochastic processes arising in statistical physics. Examples include: interacting particle systems, equilibrium and non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and symmetry breaking, conformal theories, quantum gravity, free probability, random matrices theory, and disordered systems. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic PDEs), random geometry, mathematical population genetics are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group. The section on Integrable Systems carries on the work initiated with the Journal of Integrable Systems (originally published by OUP) and focuses on new interfaces of the theory of integrable systems, both discrete and continuous, with classical and modern mathematics. This includes, but is not restricted to, algebraic geometry, differential and difference geometry, twistor theory, topology and knot theory, tropical geometry, enumerative geometry and combinatorics; Lie algebras, cluster algebras and representation theory, quantum groups and non-commutative algebras; special functions and Painlev é equations, solitons and moduli spaces, spectral theory and Riemann-Hilbert problems, probability theory and random matrix theory. .