Contents -- Introduction -- 1 The problems of the Standard Model -- 1.1 General discussion -- 1.2 Naturalness and the problem of hierarchy -- 1.3 Supersymmetry as a solution to the problem of naturalness -- 2 The singular rôle of supersymmetry -- 2.1 Why supersymmetry? -- 2.2 The supersymmetry algebra -- 2.3 Supersymmetry breaking -- 2.4 Supersymmetric quantum mechanics -- 2.5 Witten index -- 3 Basic supermultiplets -- 3.1 Chiral supermultiplet -- 3.2 Vector supermultiplet and gauge interactions -- 4 The supersymmetry algebra and its representations -- 4.1 Supersymmetry algebra -- 4.2 Supermultiplet of currents -- 4.3 Representations of the supersymmetry algebra -- 4.4 Multiplets of N = 2 supersymmetry -- 4.5 BPS states -- 5 The minimal supersymmetric model -- 5.1 Why double the number of fundamental fields? -- 5.2 Model building -- 5.3 The Minimal SuperSymmetric Model (MSSM) -- 5.4 Baryon and lepton number -- 5.5 The LSP and dark matter -- 5.6 Nonminimal models -- 6 Supergravity -- 6.1 Local supersymmetry is supergravity -- 6.2 Coupling of matter to supergravity -- 6.3 Supersymmetry breaking -- 6.4 The gravitino and Goldstino fields -- 6.5 Radiative breaking of SU(2) × U(1) -- 6.6 Gaugino masses -- 6.7 Scalar masses -- 6.8 The minimal supergravity model -- 6.9 Infrared fixed points, quasi-infrared fixed points and focus points -- 6.10 The issue of fine tuning -- 6.11 The μ problem -- 6.12 No-scale models -- 7 Phenomenology of supersymmetric models: supersymmetry at the quantum level -- 7.1 Why does the MSSM survive the electroweak precision tests? -- 7.2 The Higgs sector -- 7.3 Avoiding instabilities in the flat directions of the scalar potential -- 7.4 High-energy vs. low-energy supersymmetry breaking -- 7.5 Limits on supersymmetric particles -- 7.6 R-parity breaking -- 7.7 The issue of phases -- 8 Dynamical breaking. Duality.

8.1 Dynamical supersymmetry breaking: an overview -- 8.2 Perturbative nonrenormalization theorems -- 8.3 Key issues in dynamical breaking -- 8.4 Example of supersymmetric SU(N[sub(c)]) with N[sub(f)] flavors. The rôle of R-symmetries -- 8.5 N = 2 supersymmetry and the Seiberg-Witten model -- 9 Supersymmetric grand unification -- 9.1 An overview of grand unification -- 9.2 Gauge coupling unification -- 9.3 The minimal supersymmetric SU(5) model -- 9.4 The SO(10) model -- 9.5 E[sub(6)] -- 10 An overview of string theory and string models -- 10.1 The general string picture -- 10.2 Compactification -- 10.3 String dualities and branes -- 10.4 Phenomenological aspects of superstring models -- 11 Supersymmetry and the early Universe -- 11.1 The ultimate laboratory -- 11.2 Cosmological relevance of moduli fields -- 11.3 Inflation scenarios -- 11.4 Cosmic strings -- 11.5 Baryogenesis -- 12 The challenges of supersymmetry -- 12.1 The flavor problem -- 12.2 Cosmological constant -- Appendix A: A review of the Standard Model and of various notions of quantum field theory -- A.1 Symmetries -- A.2 Spontaneous breaking of symmetry -- A.3 The Standard Model of electroweak interactions -- A.4 Electroweak precision tests -- A.5 Dilatations and renormalization group -- A.6 Axial anomaly -- Appendix B: Spinors -- B.1 Spinors in four dimensions -- B.2 Spinors in higher dimensions -- Appendix C: Superfields -- C.1 Superspace and superfields -- C.2 The chiral superfield -- C.3 The vector superfield -- C.4 The linear superfield -- Appendix D: An introduction to cosmology -- D.1 Elements of general relativity -- D.2 Friedmann-Robertson-Walker Universes -- D.3 The hot Big Bang scenario -- D.4 Inflationary cosmology -- D.5 Cosmic strings -- Appendix E: Renormalization group equations -- E.1 Gauge couplings -- E.2 μ parameter -- E.3 Anomalous dimensions -- E.4 Yukawa couplings.

E.5 Gaugino masses -- E.6 Soft scalar masses -- E.7 A-terms -- E.8 Dimensional reduction -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y.