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The lecture notes give an overview of modern cosmology: After introducing the necessary concepts from general relativity, the FLRW-class of cosmological models is discussed, with emphasis on dark energy. Cosmic structure formation, the necessity of dark matter and the interplay between statistics and nonlinear fluid mechanics are treated in detail. The physics behind cosmological observations that have led to the standard model of cosmology is explained, in particular supernovae, the cosmic microwave background and gravitational lensing.