Fa\`a di Bruno Hopf algebras
  This is a short review on the Fa\`a di Bruno formulas, and some Hopf algebras associated to them. These allow, among several other things, a short proof of the Lie-Scheffers theorem, and relating the Lagrange inversion formulas with antipodes. The link of Fa\`a di Bruno formulas with the theory of set partitions is developed in some detail. 
H\'ector Figueroa, Jos\'e M. Gracia-Bond\'ia and Joseph C. V\'arilly