A (classical) knot is an embedding of S^1 into S^3 or R^3. Less formally, it's a simple closed curve just chillin' in space. They're spicy circles! Knot theory is the study of these spicy circles. Knot theorists are interested in distinguishing knots, and there are many tools we use to do so. These tools are called invariants, and they come in many flavors.

At each crossing of a classical knot, you can see where the knot goes over or under (but never through!) itself. These are classical crossings. If you see a knot in the wild that is missing this "over-under" information at a crossing, congratulations! You may have spotted a virtual knot!

A virtual knot is a generalization of a classical knot. There are a few different ways to understand what a virtual knot is.

1. as a knot with unknown "over-under" information at at least one crossing

2. as a knot that results from a Gauss Code/Diagram that forces you to introduce a new crossing (if that means anything to you!)

3. as a knot that must live in a surface of positive genus

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