Before we look at what knot theory is, we must first understand what we mean when we are talking about a “knot” in this context. We define a knot as a closed curve in three dimensional space that does not intersect itself. If you imagine tying a knot in a piece of string and gluing the loose ends together, you would get a knot in the sense of the objects we are working with.
Knot Theory then, is the study of the properties of knots. In particular, we are interested in the properties of knots that don’t change when we deform the knot (without cutting or intersecting). These properties are referred to as Knot Invariants. From these invariants, we can make decisions as to whether a given knot is the same as another.
Rational Tangles and Braids Undergraduate Research 