The field of Cosmology is currently undergoing a revolution driven by dramatic observational progresses and by novel theoretical scenarios imported from particle physics. This book contains lectures by world experts in the various branches of this field corresponding to lectures presented during the School "Frontiers of the Universe" at the IESC, (Corsica,France). These pedagogical lectures cover major subjects relevant to the field ( inflation; CMB: anisotropies and polarization; quintessence/dark energy; inflation; CMB: anisotropies and polarization; clusters of galaxies; gravitational lensing; galaxy formation; dark matter; supernovae and the accelerating expansion of the Universe), providing invaluable introductory material appropriate to PhD students as well as to more senior scientists who wish to become familiar with the various domains of the modern developments in Cosmology