Contents: Supermembranes & Supersymmetric Matrix Models (H Nicolai); Introduction to D-Brane Technology (C Johnson); Matrix String Theory (H Verlinde); Substringy Geometry (M Douglas); Phenomenological Aspects of String Theory (J Louis); Branes & the AdS Super-gravity (S Randjbar-Daemi); F-Theory (B Greene); Gauge Theory & AdS Supergravity (S Kachru); Conformal Theory on Branes (R Kallosh); 4-D CFT & Strings on Orbifolds (S Kachru); Brane Solutions in M(atrix) Theory (S Randjbar-Daemi); Some Properties of Six-Dimensional (1, 0) Super Gravity (A Sagnotti); Brane Twisters (C Pope); Branes & Super Embeddings (P Howe); On Some Features of the M 5-Brane (D Sorokin); 5 Brane Dynamics & Four-Dimensional QFT (P West); Anti-de-Sitter Space, Branes, Singletons, Super CFT & All That (M Duff); Brane-Singleton Connection Revisited (E Sezgin); Maldecena's Conjecture & the Large-N Behaviour of Matrix Theory (L Susskind); Limits of M-Theory & Limitations of Matrix Theory (C Hull); The Universe as a Domain Wall (K Stelle); SL(2, Z) Family of Type 2B Superfivebranes (J Lu); String on SL(2, R) (J Evans); & other papers. Readership: Researchers in string theory & supersymmetric field theory.

In chapter 1 the author reviews some elements of string theory relevant to the rest of this report. He touches on both the classical, i.e. perturbative, string physics before D-branes rise to prominence, and some of the progresses they brought forth. In chapter 2 he proceeds to give an exact algebraic formulation of D-branes in curved spaces. This allows one to classify them in backgrounds of interest and study their geometric properties. He applies this formalism to string theory on Calabi-Yau and other supersymmetry preserving manifolds. Then he studies the behavior of the D-branes under mirror symmetry in chapter 3. Mirror symmetry is known to be a symmetry of string theory perturbatively. He finds evidence for its nonperturbative validity when D-branes are also considered and compute some dynamical consequences. In chapter 4 he turns to examine the consistency of curved and/or intersecting D-brane configurations. They have been used recently to extract information about the field theories that arise in certain limits. It turns out that there are potential quantum mechanical inconsistencies associated with them. What saves the day are certain subtle topological properties of D-branes. This resolution has implications for the conserved charges carried by the D-branes, which he computes for the cases studied in chapter 2. In chapter 5 he uses intersecting brane configurations to study three dimensional supersymmetric gauge theories. There is also a mirror symmetry there that, among other things, exchanges classical and quantum mechanical quantities of a (mirror) pair of theories. It has an elegant realization in term of a symmetry of string theory involving D-branes. The author employs it to study a wide class of 3d models. He also predicts new mirror pairs and unconventional 3d field theories without Lagrangian descriptions.

As recent developments have shown, supersymmetric quantum field theory and string theory are intimately related, with advances in one area often shedding light on the other. The organising ideas of most of these advances are the notion of duality and the physics of higher dimensional objects or p-branes. The topics covered in the present volume include duality in field theory, in particular in supersymmetric field theory and supergravity, and in string theory. The Seiberg-Witten theory and its recent developments are also covered in detail. A large fraction of the volume is devoted to the current state of the art in M-theory, in particular its underlying superalgebra as well as its connection with superstring and N = 2 strings. The physics of D-branes and its essential role in the beautiful computation of the black hole entropy is also carefully covered. Finally, the last two sets of lectures are devoted to the exciting matrix approach to non-perturbative string theory.

Many of the topics in this book are outgrowths of the spectacular new understanding of duality in string theory which emerged around 1995. They include the AdS/CFT correspondence and its relation to holography, the matrix theory formulation of M theory, the structure of black holes in string theory, the structure of D-branes and M-branes, and detailed development of dualities with N = 1 and N = 2 supersymmetry. In addition, there are lectures covering experimental and phenomenological aspects of the Standard Model and its extensions, and discussions on cosmology including both theoretical aspects and the exciting new experimental evidence for a non-zero cosmological constant.

Detailed, step-by-step introduction to the theoretical foundations of strings and branes, essential reading for graduate students and researchers.