Steenrod and Dyer-Lashof operations on $B{\bf U}$

This paper describes a simple, fast algorithm for the computation of Steenrod and Dyer-Lashof operations on BU. The calculations are carried out in H*(BU, Z(P)) and H*(BU, Z(P)) where p local lifts are determined by the values on primitives and Cartan formulas. This algorithm also provides a description of Steenrod and Dyer-Lashof operations on the fiber of any H map (or infinite loop map) BU -BU, and applications to the classifying spaces of surgery which arise in this fashion will appear shortly.