Includes bibliographical references.

Part I. Introduction: 1. Introduction and guide to the Handbook / G. Akenmann, J. Baik and P. Di Francesco; 2. History: an overview / O. Bohigas and H.A. Weidenmüller -- Part II. Properties of Random Matrix Theory: 3. Symmetry classes / M.R. Zirnbauer; 4. Spectral statisitics of unitary emsembles / G.W. Anderson; 5. Spectral statistics of orthogonal and symplectic ensembles / M. Adler; 6. Universality / A.B.J. Kuijlaars; 7. Supersymmetry / T. Guhr; 8. Replica approach in random matrix theory / E. Kanzieper; 9. Painlevé transcendents / A.R. Its; 10. Random matrix theory and Integrable systems / P. van Moerbeke; 11. Determinantal point processes / A. Borodin; 12. Random matrix representations of critical statistics / V.E. Kravtsov; 13. Heavy-tailed random matrices / Z. Burda and J. Jurkiewicz; 14. Phase transitions / G.M. Cicuta and L.G. Molinari; 15. Two-matrix models and biorthogonal polynomials / M. Bertola; 16. Chain of matricies, loop equations and topological recursion / N. Orantin; 17. Unitary integrals and related matrix models / A. Morozov; 18. Non-Hermitian ensembles / B.A. Khoruzhenko and H.-J. Sommers; 19. Characteristic polynomials / E. Brézin and S. Hikami; 20. Beta ensembles / P.J. Forrester; 21. Wigner matrices / G. Ben Arous and A. Guionnet; 22. Free probability theory / R. Speicher; 23. Random banded and sparse matrices / T. Spencer -- Part III. Applications of Random Matrix Theory: 24. Number theory / J.P. Keating and N.C. Snaith; 25. Random permutations and related topics / G. Olshanski; 26. Enumeration of maps / J. Bouttier; 27. Knot theory and matrix integrals / P. Zinn-Justin and J.-B. Zuber; 28. Multivariate statistics / N. El Karoui; 29. Algrebraic geometry and matrix models / L.O. Chekhov; 30. Two-dimensional quantum gravity / I. Kostov; 31. String theory / M. Mariño; 32. Quantum chromodynamics / J.J.M. Verbaarschot; 33. Quantum chaos and quantum graphs / S. Müller and M. Sieber; 34. Resonance scattering of waves in chaotic systems / Y.V. Fyodorov and D.V. Savin; 35. Condensed matter physics / C.W.J. Beenakker; 36. Classical and quantum optics / C.W.J. Beenakker; 37. Extreme eigenvalues of Wishart matrices: application to entangled bipartite system / S.N. Majumdar; 38. Random growth models / P.L. Ferrari and H. Spohn; 39. Random matrices and Laplacian growth / A. Zabrodin; 40. Financial applications of random matrix theory: a short review / J.-P. Bouchard and M. Potters; 41. Asymptotic singular value distributions in information theory / A.M. Tulino and S. Verdú; 42. Random matrix theory and ribonucleic acid (RNA) folding / G. Vernizzi and H. Orland; 43. Complex networks / G.J. Rodgers and T. Nagao.

"With a foreword by Freeman Dyson, the handbook brings together leading mathematicians and physicists to offer a comprehensive overview of random matrix theory, including a guide to new developments and the diverse range of applications of this approach. In part one, all modern and classical techniques of solving random matrix models are explored, including orthogonal polynomials, exact replicas or supersymmetry. Further, all main extensions of the classical Gaussian ensembles of Wigner and Dyson are introduced including sparse, heavy tailed, non-Hermitian or multi-matrix models. In the second and larger part, all major applications are covered, in disciplines ranging from physics and mathematics to biology and engineering. This includes standard fields such as number theory, quantum chaos or quantum chromodynamics, as well as recent developments such as partitions, growth models, knot theory, wireless communication or bio-polymer folding. The handbook is suitable both for introducing novices to this area of research and as a main source of reference for active researchers in mathematics, physics and engineering"--