Single-layer graphite oxide can be viewed as an unconventional type of soft material and has recently been recognized as a promising material for composite and electronics applications. It is of both scientific curiosity and technical importance to know how these atomically thin sheets assemble. There are two fundamental geometries of interacting single layers: edge-to-edge and face-to-face. Such interactions were studied at the air-water interface by Langmuir-Blodgett assembly. Stable monolayers of graphite oxide single layers were obtained without the need for any surfactant or stabilizing agent, due to the strong electrostatic repulsion between the 2D confined layers. Such repulsion also prevented the single layers from overlapping during compression, leading to excellent reversibility of the monolayers. In contrast to molecular and hard colloidal particle monolayers, the single layers tend to fold and wrinkle at edges to resist collapsing into multilayers. The monolayers can be transferred to a substrate, readily creating a large area of flat graphite oxide single layers. The density of such films can be continuously tuned from dilute, close-packed to overpacked monolayers of interlocking single layers. For size-mismatched single layers, face-to-face interaction caused irreversible stacking, leading to double layers. The graphite oxide monolayers can be chemically reduced to graphene for electronic applications such as transparent conducting thin films.