George Ellis, FRS, is Professor Emeritus at the University of Cape Town, South Africa. He is co-author with Stephen Hawking of The Large Scale Structure of Space-Time. Roy Maartens holds an SKA Research Chair at the University of the Western Cape, South Africa, and is Professor of Cosmology at the University of Portsmouth, UK. Malcolm MacCallum is Director of the Heilbronn Institute at the University of Bristol and is President of the International Society on General Relativity and Gravitation.

• Part I. Foundations: 1. The nature of cosmology; 2. Geometry; 3. Classical physics and gravity; Part II. Relativistic Cosmological Models: 4. Kinematics of cosmological models; 5. Matter in the Universe; 6. Dynamics of cosmological models; 7. Observations in cosmological models; 8. Light-cone approach to relativistic cosmology; Part III. The Standard Model and Extensions: 9. Homogeneous FLRW universes; 10. Perturbations of FLRW universes; 11. The cosmic background radiation; 12. Structure formation and gravitational lensing; 13. Confronting the Standard Model with observations; 14. Acceleration from dark energy or modified gravity; 15. 'Acceleration' from large scale inhomogeneity?; 16. 'Acceleration' from small scale inhomogeneity?; Part IV. Anisotropic and Inhomogeneous Models: 17. The space of cosmological models; 18. Spatially homogeneous anisotropic models; 19. Inhomogeneous models; Part V. Broader Perspective: 20. Quantum gravity and the start of the Universe; 21. Cosmology in a larger setting; 22. Conclusion: our picture of the Universe; Appendix; References; Index.

"… fills a gap in the existing literature on the subject. Written by three experts of General Relativity, it stresses the geometric aspects of cosmology and contains topics which are neglected in most texts on the subject: it discusses fundamental issues like the Copernican principle and the light-cone approach to cosmological observations. I like especially Part 3, where gauge-invariant, covariant cosmological perturbation theory is employed to study structure formation, fluctuations in the cosmic microwave background and different aspects of the Dark Energy problem including, especially a thorough discussion of backreaction. Finally, anisotropic and inhomogeneous models are presented, which at the present status of cosmology research, may turn out to be more than an academic exercise. This text, which always stresses the open questions on each given topic is very valuable and timely for graduate students and researchers in the field. Especially in view of the ’Dark Energy challenge’ which requires that we explore all avenues which may shed light in the bizarre apparent acceleration of cosmic expansion. The book helps us to take the necessary step back and re-consider the fundamental assumptions which go into the present cosmological standard model." Ruth Durrer, University of Geneva