纽结理论是拓扑学的一个分支，研究纽结的拓扑学特性。

结绳纪事由来远古，但从数学上研究纽结，始于德国数学家卡尔·弗里德里希·高斯，高斯研究电磁场的性质，认为与纽结有关。1867年凯尔文勋爵认为原子是以太漩涡的纽结，可用不同种类的纽结将原子分类，并用来解释为何原子的吸收光谱呈现不连续的现象。

苏格兰理论物理学家彼德·G·泰特用多年时间研究出纽结分类表，相信他正在创造一个元素表。1887年迈克耳孙-莫雷实验证明“以太”不存在，“以太漩涡论”成为过时理论。十九世纪末叶，产生拓扑学，纽结论再此成为热点研究课题。今日纽结论的应用包括弦理论、DNA复制和统计力学等领域。

In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R (in topology, a circle isn't bound to the classical geometric concept, but to all of its homeomorphisms). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself.