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.

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.

Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.

This invaluable book provides a quick introduction to the rudiments of perturbative string theory and a detailed introduction to the more current topic of D-brane dynamics. The presentation is very pedagogical, with much of the technical detail streamlined. The rapid but highly coherent introduction to the subject is perhaps what distinguishes this book from other string theory or D-brane books. This second edition includes an additional appendix with solutions to the exercises, thus expanding on some of the technical material and making the book more appealing for use in lecture courses. The material is based on mini-courses in theoretical high energy physics delivered by the author at various summer schools, so its actual level has been appropriately tested./a