A multiple window display system is provided for displaying data from different applications in a multi-tasking environment. The display system includes plural screen buffers (12.sub.l to 12.sub.n) for storing character codes and attribute codes of data which may be displayed on the display screen. Task selection means (26) selectively couples the output of a single selected one of the plural screen buffers to the character generator (16) and attribute logic (18) at any given time. Address modification means (20.sub.l to 20.sub.n, 22.sub.l to 22.sub.n) permits changes to be made in the display windows. The software driver includes screen control blocks (32), window control blocks (34), presentation space control blocks (36), presentation spaces (38), and a screen matrix (40) in system memory. The presentation spaces (38) receive application data for plural windows of the displayable area. Each window defines the whole or a subset of a corresponding presentation space. The screen matrix (40) is mapped to the display screen and filters data from the windows of the presentation spaces to the screen buffer to designate which of the data will be shown in corresponding positions on the display screen.