  We present an algebraic algorithm that computes the composition of two power
series in $\mathop{\tilde{\mathrm O}}(n)$ time complexity. The previous best
algorithms are $\mathop{\mathrm O}(n^{1+o(1)})$ by Kedlaya and Umans (FOCS
2008) and an $\mathop{\mathrm O}(n^{1.43})$ algebraic algorithm by Neiger,
Salvy, Schost and Villard (JACM 2023).
  Our algorithm builds upon the recent Graeffe iteration approach to manipulate
rational power series introduced by Bostan and Mori (SOSA 2021).
