超运算串行，是数学中一种二元运算的串行，前几项分别为加法、乘法、幂、迭代幂次，这些运算通称为超运算（或称为hyper运算符）。串行的第n项称为超-n运算。英文则由鲁宾·古德斯坦（Reuben Goodstein）命名，由n的希腊语前缀加上后缀-ation组成（例如超-4运算称为tetration，超-5运算称为pentation）。使用高德纳箭号表示法可将超运算算子表示为(n-2)个箭头。

超运算可通过递归进行定义，使用阿克曼函数的递归法则可以得到定义（部分）：

除这一最常见的定义之外，超运算还有其他的变体。（见下文）

In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations) that starts with the unary operation of successor (n = 0), then continues with the binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3), after which the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity. For the operations beyond exponentiation, the nth member of this sequence is named by Reuben Goodstein after the Greek prefix of n suffixed with -ation (such as tetration (n = 4), pentation (n = 5), hexation (n = 6), etc.) and can be written as using n − 2 arrows in Knuth's up-arrow notation. Each hyperoperation may be understood recursively in terms of the previous one by: