  In this note we present the classification of non-symplectic automorphisms of
prime order on K3 surfaces, i.e.we describe the topological structure of their
fixed locus and determine the invariant lattice in cohomology. We provide new
results for automorphisms of order 5 and 7 and alternative proofs for higher
orders. Moreover, for any prime p, we identify the irreducible components of
the moduli space of K3 surfaces with a non-symplectic automorphism of order p.
