Abstract: At least one hollow core tower (preferably of a rectangular construction) is constructed from a foundation to a preselected floor supporting height. The tower is preferably joined at the top and slotted vertically along at least one sidewall from the base of the tower to a partial height of the tower. Preferably the tower is slotted along opposed sidewalls to form opposed C-shaped sections confronting one another at the slots. After at least the lowest and ground adjacent portion of the tower is constructed, floors are built about the tower at or near ground level. The floors include a section extending into or across the tower at the slot or slots which preferably includes a cantilevered or spanning horizontal floor strengthening beam. Typically, the floors are constructed and stacked one on another at their ground level with the bottom floor built first and lowest, and the top floor or roof built last and highest at the top of the ground supported stack.