  We construct stable Adams operations on the cohomology theory Tmf of
topological modular forms. This is done by extending the sheaf defining Tmf to
be functorial with respect to isogenies of generalised elliptic curves of
invertible degree. These Adams operations are then calculated on the homotopy
groups of Tmf using a combination of descent spectral sequences, the theory of
synthetic spectra, and Anderson duality.
