Knot invariants are properties of knots that remain unchanged under deformations, such as stretching or twisting, but not cutting. They help mathematicians classify and distinguish different knots. Common examples of knot invariants include the knot group, Alexander polynomial, and Jones polynomial. These invariants provide valuable information about the structure of knots and can be used to determine whether two knots are equivalent. By studying knot invariants, researchers can gain insights into the mathematical field of topology, which explores the properties of space that are preserved under continuous transformations.