Publisher Summary This chapter discusses intervals. Intervals are the fundamental abstraction needed for dealing with temporal data satisfactorily. The first and most fundamental step is to recognize the need to deal with intervals as such that is, the need to treat intervals as values in their own right, instead of treating them as pairs of separate values. Conventionally, therefore, an interval is denoted by a pair of points separated by a colon, preceded by an opening bracket or parenthesis and followed by a closing bracket or parenthesis. A bracket is used where one wants the closed interpretation, a parenthesis where one wants the open one. The applications for intervals are varied. Tax brackets are represented by taxable-income ranges—in other words, intervals whose begin and end points are money values. Machines are built to operate within certain temperature and voltage ranges—in other words, intervals whose contained points are temperatures and voltages, respectively. Animals vary in the range of frequencies of light and sound waves to which their eyes and ears are receptive. Various natural phenomena occur and can be measured in ranges in depth of soil or sea or height above sea level.