In the mathematical theory of knots, a pretzel link is a special kind of link. It consists of a finite number tangles made of two intertwined circular helices, The tangles are connected cyclicly, the first component of the first tangle is connected to the second component of the second tangle, etc., with the first component of the last tangle connected to the second component of the first. A pretzel link which is also a knot (i.e. a link with one component) is a pretzel knot.
Each tangle is characterized by its number of twists, positive if they are counter-clockwise or left-handed, negative if clockwise or right-handed. In the standard projection of the pretzel link, there are left-handed crossings in the first |tangle, in the second, and, in general, in the nth.
A pretzel link can also be described as a Montesinos link with integer tangles.
A Montesinos link is a special kind of link that generalizes pretzel links (a pretzel link can also be described as a Montesinos link with integer tangles). A Montesinos link which is also a knot (i.e., a link with one component) is a Montesinos knot.
A Montesinos link is composed of several rational tangles. One notation for a Montesinos link is .
In this notation, and all the and are integers. The Montesinos link given by this notation consists of the sum of the rational tangles given by the integer and the rational tangles
The hyperbolic volume of the complement of the (−2,3,8) pretzel link is 4 times Catalan's constant, approximately 3.66. This pretzel link complement is one of two two-cusped hyperbolic manifolds with the minimum possible volume, the other being the complement of the Whitehead link.