1 / Introduction.- 1.1. Historical Background.- 1.2. What This Book is About.- I Quantum Theory.

- 2 / Path Integrals.- 2.1. Action in Classical Physics.- 2.2. Action in Quantum Physics.- 2.

3. The Path Integral.- 2.4. The Quadratic Action.- 2.5. The Schrödinger Equation.

- 2.6. The Spreading of Wave Packets.- 2.7. The Harmonic Oscillator.- Notes and References.- 3 / En Route to Quantum Field Theory.

- 3.1. The Field as a Dynamical System.- 3.2. Harmonic Oscillator in an External Potential.- 3.3.

The Vacuum Persistence Amplitude.- 3.4. Euclidean Time.- 3.5. The Double-Hump Potential.- 3.

6. The Instanton Solutions.- 3.7. The Concept of an Effective Action.- 3.8. Quantum Mechanics at Finite Temperature.

- Notes and References.- 4 / Quantum Field Theory.- 4.1. Classical Field Theory (General).- 4.2. Classical Field Theory (Specific Fields).

- 4.3. Quantization of the Scalar Field.- 4.4. Canonical Quantization.- 4.5.

Scalar Field with Quartic Self-interaction.- 4.6. Nonperturbative Methods.- 4.7. Quantum Theory in External Fields.- 4.

8. Field Theory at Finite Temperature.- Notes and References.- 5 / Gauge Fields.- 5.1. Gauge Invariance -- Electromagnetism.- 5.

2. Gauge Invariance -- Generalized.- 5.3. General Formalism for Gauge Theory.- 5.4. Spontaneous Symmetry Breaking.

- 5.5. SSB with an Abelian Gauge Field.- 5.6. SSB with a Nonabelian Gauge Field.- 5.7.

The Salam--Weinberg Model.- 5.8. The Coleman--Weinberg Mechanism.- 5.9. The Gauge Field as a Physical System.- 5.

10. The Gauge Field Vacuum and Instantons.- 5.11. Solitons -- Monopole Solution.- Notes and References.- II Classical General Relativity.- 6 / General Theory of Relativity.

- 6.1. The Need for a General Theory of Relativity.- 6.2. Curved Spacetime.- 6.3.

Vectors and Tensors.- 6.4. Metric and Geodesics.- 6.5. Parallel Transport.- 6.

6. The Curvature Tensor.- 6.7. Physics in Curved Spacetime.- 6.8. Einstein''s Field Equations.

- 6.9. The Newtonian Approximation.- 6.10. The ? Term.- 6.11 Conformal Transformations.

- Notes and References.- 7 / Gravitating Massive Objects.- 7.1. The Schwarzschild Solution.- 7.2. Experimental Tests of General Relativity.

- 7.3. Gravitational Radiation.- 7.4. Geometrodynamics.- 7.5.

Gravitational Collapse.- 7.6. Black Holes.- Notes and References.- 8 / Relativistic Cosmology.- 8.1.

Cosmological Symmetries.- 8.2. The Friedmann Models.- 8.3. Observational Cosmology.- 8.

4. The Early Universe.- 8.5. The Problems of Singularity, Horizon, and Flatness.- 8.6. Anisotropic Cosmologies.

- Notes and References.- III Quantization in Curved Spacetime.- 9 / Quantum Theory in Curved Spacetime.- 9.1. Quantum Theory in a Curved Background: Why?.- 9.2.

General Covariance and the Particle Concept.- 9.3. Field Theory in Robertson-Walker Spacetime.- 9.4. Field Theory in de Sitter Spacetime.- 9.

5. Euclideanization and the Thermal Green''s Functions.- 9.6. Field Theory in the Black-Hole Spacetime.- Notes and References.- 10 / The Very Early Universe.- 10.

1. Symmetry Breaking in the Early Universe.- 10.2. Cosmological Monopoles.- 10.3. Cosmological Inflationary Scenarios.

- 10.4. The Guth Inflation.- 10.5. Inflation with the Coleman--Weinberg Potential.- 10.6.

Fine-Tunings in the Early Universe.- Notes and References.- IV Quantum Cosmology.- 11 / Approaches to Quantum Cosmology.- 11.1. Introduction.- 11.

2. The Linearized Theory.- 11.3. Canonical Quantization.- 11.4. Manifestly Covariant Quantization.

- 11.5. Path Integrals in Euclidean Spacetime.- 11.6. Concluding Remarks.- Notes and References.- 12 / Quantum Conformal Fluctuations.

- 12.1. Quantum Gravity via Path Integrals.- 12.2. Conformal Fluctuations.- 12.3.

QCF of Friedmann Cosmologies.- 12.4. Bianchi Type I Cosmologies.- 12.5. Universes with Arbitrary Distributions of Massive Particles.- 12.

6. The Problems of Singularity and Horizons.- 12.7. The Problem of Flatness.- 12.8. Further Developments.

- Notes and References.- 13 / Towards a More Complete Theory.- 13.1. Towards a More Complete Theory.- 13.2. The Average Metric.

- 13.3. Quantum Fluctuations and Proper Length.- 13.4. Lower Bound to Proper Length.- 13.5.

Quantum Stationary Geometries.- 13.6. QSG and the Back Reaction on the Metric.- 13.7. Solutions of Quantum Gravity Equations.- 13.

8. Cosmogenesis and Vacuum Instability.- Notes and References.- 14 / Epilogue.- V Appendices.- Appendix A/Renormalization.- Appendix B/Basic Group Theory.- B.

1. Definition of a Group.- B.2. Generators.- B.3. Representations.

- Appendix C/Differential Geometry.- C.1. Basic Concepts.- C.2. Vectors and 1-Forms.- C.

3. Lie Derivative and Covariant Derivative.- C.4. Curvature and Metric.- Appendix D/Spacetime Symmetries.- D.1.

Displacement of Spacetime.- D.2. Killing Vectors.- D.3. Homogeneity.- D.

4. Isotropy.