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A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics. Preface J. Wess. Gauge Theories Beyond Gauge Theory D. Leites, V. Serganova. Symmetries Wider Than Supersymmetry K. Stelle. Tensions in Supergravity Braneworlds P. Grozman, D. Leites An Unconventional Supergravity E. Bergshoeff, R. Kallosh, A. Van Proeyen. Supersymmetry Of RS Bulk And Brane D. Galtsov, V. Dyadichev. D-branes And Vacuum Periodicity P. Kosi ´ nski, J. Lukierski, P. Ma´slanka. Quantum Deformations Of Space-Time SUSY And Noncommutative Superfield Theory D. Leites, I. Shchepochkina. The Howe Duality And Lie Superalgebras A. Sergeev. Enveloping Algebra Of GL(3) And Orthogonal Polynomials S. Duplij, W. Marcinek. Noninvertibility, Semisupermanifolds And Categories Regularization F. Brandt. An Overview Of New Supersymmetric Gauge Theories With 2-Form Gauge Potentials K. Peeters, P. Vanhove, A. Westerberg. Supersymmetric R4 Actions And Quantum Corrections To Superspace Torsion Constraints S. Fedoruk, V. G. Zima. Massive Superparticle With Spinorial Central Charges A. Burinskii. Rotating Super Black Hole as Spinning Particle F. Toppan. Classifying N-extended 1-dimensional Super Systems C. Quesne. Para, Pseudo, And Orthosupersymmetric Quantum Mechanics And Their Bosonization A. Frydryszak. Supersymmetric Odd Mechanical Systems And Hilbert Q-module Quantization S. Vacaru, I. Chiosa, N. Vicol. Locally Anisotropic Supergravity And Gauge Gravity On Noncommutative Spaces T. Kobayashi, J. Kubo, M. Mondrag´on, G. Zoupanos. Finiteness In Conventional N = 1 GUTs