Eta invariant and analytic torsion are the two prominent spectral invariants arising from index theory. Both are secondary invariants. The eta invariant is the boundary contribution to the index formula and measures the spectral asymmetry. The analytic torsion, on the other hand, is a certain combination of determinants of Laplacians, and gives analytic interpretation of the Reidemeister torsion, a topological invariant which is not homotopy invariant (and hence is very useful in finer classifications). Each has higher dimensional generalizations and noncommutative geometric extensions. In this talk, I will review these developments and discuss  our work with Weiping Zhang on the relation between these two invariants.

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