Abstract: A building constructed mainly of a series of modular units permanently united to each other. Various different forms of units are provided, and units of different forms may be arranged in various different relations to each other, to provide a choice of floor plans. Each unit is a rigid structure having a floor slab portion and one or more wall portions integrally connected to the floor slab portion and rising to the full height of the story, at least some of the wall portions of most of the units being offset laterally inwardly from the edges of the floor slab portion. When various units of the same story are assembled in side by side relation, the wall portion or portions of one unit cooperate with the wall portion or portions of one or more additional units to provide an enclosure constituting a room. The floor slab portions of the next higher story rest on the top edges of the wall portions of the story immediately below.