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But the title says "... and its Applications". Is tying actual knots not an application of knot theory?

The applications mentioned in the book are to chemistry and to molecular biology. (As well as another, mentioned only fairly briefly, elsewhere in pure mathematics, to what's called the classification of 3-manifolds.)

No, tying knots isn't an application of knot theory. To learn about some applications of knot theory, you could read the textbook in the OP.

It is absolutely related, though most real world things we call knots are usually in fact closer to tangles or links with the ends of the rope looping back to the other end virtually.

Neck ties are a mathematical knot if you again assume the two ends are connected. See other comment in this thread.

Knot theory here only determines the "shapes" of the knots and which are "allowed", there is no friction, width, etc.

https://en.m.wikipedia.org/wiki/Link_(knot_theory)

https://math.stackexchange.com/questions/217670/is-there-a-m...

https://en.m.wikipedia.org/wiki/Physical_knot_theory

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