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This review article is devoted to analyze the main properties characterizingthe cosmological singularity associated to the homogeneous and inhomogeneousMixmaster model. After the introduction of the main tools required to treat thecosmological issue, we review in details the main results got along the lastforty years on the Mixmaster topic. We firstly assess the classical picture ofthe homogeneous chaotic cosmologies and, after a presentation of the canonicalmethod for the quantization, we develop the quantum Mixmaster behavior.Finally, we extend both the classical and quantum features to the fullyinhomogeneous case. Our survey analyzes the fundamental framework of theMixmaster picture and completes it by accounting for recent and peculiaroutstanding results.

Classical and Quantum Features of the Mixmaster Singularity