Dedication, Preface Acknowledgments;

1 Basics of Cosmology Monique Signore, Alain Blanchard

1. Geometry and Dynamics ; 2.Important quantities needed for observations

3. Some solutions of EFL equations:some cosmological models; 4. The standard Big Bang Nucleosynthesis (SBBN);5. Observations of ``primordial abundances'; 6. Confrontation of the observed ``primordial abundances'' to the predictions of the sBBN; Conclusions; References

2 X-ray View of Galaxy Clusters, William Forman

1. Observing Clusters in X-rays -- the Chandra Observatory;2. Regular Clusters XD Cooling Flows A478;3. Physics of Cluster Cores; Acknowledgments; References;

3 Clusters: an optical point of view; Christophe Adami

1. Cluster detections in the optical;2. Studies of clusters;3. Acknowledgements;References

4 Cosmology with Clusters; Alain Blanchard

1. Introduction;2. What is a cluster? ; 3. The spherical model;4. The mass function;

5. Connection to the observations; 6. Properties of Clusters and scaling relations; 7. Clusters abundance evolution; 8. The baryon fraction; 9. Conclusion; References

5 Astrophysical detection of Dark Matter ; S. Colafrancesco;

1. Signals from the Dark universe ; 2. Inference probes;3. Physical probes;4. Conclusion; References

6 Non-thermal processes in galaxy clusters ; S. Colafrancesco

1. Non-thermal and relativistic phenomena in galaxy clusters;2. The origin of cosmic rays in galaxy clusters; 3. The astrophysics of cosmic rays in galaxy clusters ; 4. Conclusions; References

7 Cosmological Inflation ; Alain Riazuelo

1. Introduction; 2. The hot Big-Bang scenario and its problems ;3. Inflation and inflationary dynamics;4. Basics of cosmological perturbations ;Synchronous gauge;Longitudinal or Newtonian gauge; Flat-slicing gauge ; 5. Inflationary perturbations; 6. Basics of quantum field theory;7. Perturbation spectrum; 8. Conclusion; References

8 An introduction to quintessence ; Alain Riazuelo

1. The two cosmological constant problems;2. A scalar field as dark energy;3. Stability of the w_{Q }= Const regime ;4. Model building;5. Dark energy and structure formation; 6. Observational status; References

9 CMB Observational Techniques and Recent Results

1. Introduction;2. Observational Techniques ;3. Recent Observations; 4. Summary; Acknowledgments; References;

10 Fluctuations in the CMB ; Andrew H. Jaffe

1. Introduction;2. Cosmological Preliminaries; 3. The Last Scattering Surface ; 4. Perturbations on Large and Small Scales;5. Oscillations in the Primordial Plasma;6. The Power Spectrum of CMB Fluctuations;7. The CMB and Cosmological Parameters;8. Conclusions; Acknowledgments; References

11 Supernovae as astrophysical objects; Bruno Leibundgut

1. Some History;2. Supernova classification;3. Input Energy;4. Core-collapse supernovae ;

5. Type Ia supernovae ;6. Conclusions; References

12 Cosmology with Supernovae ; Bruno Leibundgut

1. Introduction;2. The Hubble constant;3. The expansion history of the universe;4. Universal acceleration according to Type Ia supernovae ;5. Characterising dark energy ;6. Conclusions; References

13 Gravitational lensing; Francis Bernardeau

1. Introduction;2. Physical mechanisms; Multiple images and displacement field;The amplification matrix ;3. Gravitational lenses in Cosmology;The case of a spherically symmetric mass distribution;Critical lines and caustics in realistic mass distributions; 4. Cosmic Shear: weak lensing as a probe of the large-scale structure;5. Conclusions and perspectives: cosmic shear in a precision;Cosmology era; References

14 Dark Matter ; Jaan Einasto

1. Introduction;2. Local Dark Matter;3. Clusters and Groups of Galaxies;4. Masses of Galaxies ;

5. The Nature of Dark Matter;6. Summary;Acknowledgments;References

15 Dark Matter and Galaxy Formation;Joseph Silk

1. Challenges of dark matter;2. Global baryon inventory;3. Confirmation via detailed census of MWG/M31; 4. Hierarchical galaxy formation;5. Unresolved issues in galaxy formation theory; 6. Resurrecting CDM ;7. An astrophysical solution: early winds;8. Observing CDM via the WIMP LSP; 9. The future ; References

16 Non-Baryonic Dark Matter; Paolo Gondolo

1. The need for non-baryonic dark matter;2. Popular candidates for non-baryonic dark matter; 3. Neutralino dark matter searches; High energy neutrinos from the core of the Sun or of the Earth; Gamma-rays and cosmic rays from neutralino annihilation in galactic halos;Signals from neutralino annihilation at the Galactic Center; 4. Conclusions ; References