The $n$ in $n$-space represents a natural number i.e. $n \in \mathbb{N}$ The $n$-space is a higher dimesional space of order $n$. The idea of using ordered pairs and triples of real numbers to represent points in twodimensional space and three-dimensional space was well known in the eighteenth and nineteenth centuries. By the dawn of the twentieth century, mathematicians and physicists were exploring the use of "higher dimensional" spaces in mathematics and physics. Today, even the layman is familiar with the notion of time as a fourth dimension, an idea used by Albert Einstein in developing the general theory of relativity. Today, physicists working in the field of "string theory" commonly use 11 -dimensional space in their quest for a unified theory that will explain how the fundamental forces of nature work. Much of the remaining work in this section is concerned with extending the notion of space to $n$ dimensions.