Before revision: We show that for every integer n\geq 1 there exists a graph G_n with n ^{1 + o(1)} edges such that every n-vertex planar graph is isomorphic to a subgraph of G_n.
After revision: We show that for every integer n\geq 1 there exists a graph G_n with (1+o(1))n vertices and n ^{1 + o(1)} edges such that every n-vertex planar graph is isomorphic to a subgraph of G_n.