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AbstractI am going to present an introduction into the geometric approach to Monge– Ampère operators and equations based on contact and symplectic structures of cotangent and the 1st jet bundles of a smooth manifold. This approach was developed by V. Lychagin and goes back to the ideas of E. Cartan and his successor T. Lepage. I shall try to make my talk self-contained. I also plan to discuss ...