In this talk, we first introduce the topological torsion invariants, i.e., Reidemeister-Milnor-Turaev torsion and Igusa-Klein torsion. Then we introduce the analytic torsion invariants, i.e., Ray-Singer torsion and Bismut-Lott torsion. We also talk about some geometric-topological correspondence in global differential geometry. At last, we will discuss the additivity property of torsion invariants and some open problems.

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