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Foreword Preface Notation 1 A first look at strings 1.1 Why strings? 1.2 Action principles 1.3 The open string spectrum 1.4 Closed and unoriented strings Exercises 2 Conformal field theory 2.1 Massless scalars in two dimensions 2.2 The operator product expansion 2.3 Ward identities and Noether's theorem 2.4 Conformal invariance 2.5 Free CFTs 2.6 The Virasoro algebra 2.7 Mode expansions 2.8 Vertex operators 2.9 More on states and operators Exercises 3 The Polyakov path integral 3.1 Sums over world-sheets 3.2 The Polyakov path integral 3.3 Gauge fixing 3.4 The Weyl anomaly 3.5 Scattering amplitudes 3.6 Vertex operators 3.7 Strings in curved spacetime Exercises 4 The string spectrum 4.1 Old covariant quantization 4.2 BRST quantization 4.3 BRST quantization of the string 4.4 The no-ghost theorem Exercises 5 The string S-matrix 5.1 The circle and the torus 5.2 Moduli and Riemann surfaces 5.3 The measure for moduli 5.4 More about the measure Exercises 6 Tree-level amplitudes 6.1 Riemann surfaces 6.2 Scalar expectation values 6.3 The bc CFT 6.4 The Veneziano amplitude 6.5 Chan-Paton factors and gauge interactions 6.6 Closed string tree amplitudes 6.7 General results Exercises 7 One-loop amplitudes 7.1 Riemann surfaces 7.2 CFT on the torus 7.3 The torus amplitude 7.4 Open and unoriented one-loop graphs Exercises 8 Toroidal eompaetification and T-duality 8.1 Toroidal compactification in field theory 8.2 Toroidal compactification in CFT 8.3 Closed strings and T-duality 8.4 Compactification of several dimensions 8.5 Orbifolds 8.6 Open strings 8.7 D-branes 8.8 T-duality of unoriented theories Exercises 9 Higher order amplitudes 9.1 General tree-level amplitudes 9.2 Higher genus Riemann surfaces 9.3 Sewing and cutting world-sheets 9.4 Sewing and cutting CFTs 9.5 General amplitudes 9.6 String field theory 9.7 Large order behavior 9.8 High energy and high temperature 9.9 Low dimensions and noncritical strings Exercises Appendix A: A short course on path integrals A.1 Bosonic fields A.2 Fermionic fields Exercises References Glossary Index