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Abstract：

Alongside with conic bundles, del Pezzo surfaces are possible outcomes of the Minimal Model Program ran on a geometrically rational surface. Thus, many questions about birational geometry and birational automorphisms of geometrically rational surfaces reduce to similar questions for del Pezzo surfaces. I will survey some known results concerning birational models and birational automorphism groups of del Pezzo surfaces over perfect fields, and also report on new results concerning birational geometry of del Pezzo surfaces of degree 4.