Radin Charles Miles of Tiles (367K, plain TeX) ABSTRACT. This paper is concerned with the ergodic theory of tilings of Euclidean space, in the tradition of substitution subshifts and subshifts of finite type; he main innovation being the inclusion of a natural representation of rotations in the theory. The material was given in a series of four lectures at the Workshop on Lattice Dynamics and Ergodic Theory at the University of Warwick in July 1994.