In formal language theory and computer science, a substring is a contiguous sequence of characters within a string. For instance, "the best of" is a substring of "It was the best of times". In contrast, "Itwastimes" is a subsequence of "It was the best of times", but not a substring.

Prefixes and suffixes are special cases of substrings. A prefix of a string ${\displaystyle S}$ is a substring of ${\displaystyle S}$ that occurs at the beginning of ${\displaystyle S}$; likewise, a suffix of a string ${\displaystyle S}$ is a substring that occurs at the end of ${\displaystyle S}$.

The substrings of the string "apple" would be: "a", "ap", "app", "appl", "apple", "p", "pp", "ppl", "pple", "pl", "ple", "l", "le" "e", "" (note the empty string at the end).

A string ${\displaystyle u}$ is a substring (or factor) of a string ${\displaystyle t}$ if there exists two strings ${\displaystyle p}$ and ${\displaystyle s}$ such that ${\displaystyle t=pus}$. In particular, the empty string is a substring of every string.

Example: The string ${\displaystyle u={\texttt {ana}}}$ is equal to substrings (and subsequences) of ${\displaystyle t={\texttt {banana}}}$ at two different offsets:

The first occurrence is obtained with ${\displaystyle p={\texttt {b}}}$ and ${\displaystyle s={\texttt {na}}}$, while the second occurrence is obtained with ${\displaystyle p={\texttt {ban}}}$ and ${\displaystyle s}$ being the empty string.

A substring of a string is a prefix of a suffix of the string, and equivalently a suffix of a prefix; for example, nan is a prefix of nana, which is in turn a suffix of banana. If ${\displaystyle u}$ is a substring of ${\displaystyle t}$, it is also a subsequence, which is a more general concept. The occurrences of a given pattern in a given string can be found with a string searching algorithm. Finding the longest string which is equal to a substring of two or more strings is known as the longest common substring problem. In the mathematical literature, substrings are also called subwords (in America) or factors (in Europe). ^{[citation needed]}

A string ${\displaystyle p}$ is a prefix of a string ${\displaystyle t}$ if there exists a string ${\displaystyle s}$ such that ${\displaystyle t=ps}$. A proper prefix of a string is not equal to the string itself; some sources in addition restrict a proper prefix to be non-empty. A prefix can be seen as a special case of a substring.