Knot theory is a branch of mathematics that studies the properties and classifications of knots. A knot is defined as a closed loop in three-dimensional space that does not intersect itself. Mathematicians use various techniques to determine whether two knots are equivalent, meaning one can be transformed into the other without cutting the loop. Knot theory has applications in various fields, including biology, where it helps understand the structure of DNA strands, and in physics, particularly in the study of topology and quantum mechanics. The study of knots can also lead to insights in chemistry and computer science.