A knot is an embedding of the circle into $\mathbb{R}^3$, considered
up to deformations you would expect of normal knots (made with rubber
bands (but infinitely stretchy (okay, maybe "normal" is the wrong word
(but still)))). If you were given two knots, could you deform one into
another? If the answer were always yes, you wouldn't be reading this.
We will explore a few interesting properties knots possess, and how to
distinguish them using linear algebra, differential geometry,
algebraic topology, and a whole lot more. Or less. I don't have that
much time.