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We prove that $n$-dimensional smooth hypersurfaces of degree $n+1$ aresuperrigid. Starting with the work of Fano in 1915, the proof of this Theoremtook 100 years and a dozen researchers to construct.  Here I give complete proofs, aiming to use only basic knowledge of algebraicgeometry and some Kodaira type vanishing theorems. Version 2: many changes,especially in section 1.

The rigidity theorem of Fano--Segre--Iskovskikh--Manin--Pukhlikov--Corti--Cheltsov--de Fernex--Ein--Musta\cedilla{t}\u{a}--Zhuang