Ad Introduction:
I provide a link to a very similar talk which a gave at a math conference in Islamabad in 2019. It continues a bit further into how to construct coloring invariants from transitive groups. It is not necessary to watch, I will tell you later.

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Chapter 1:

The notions you shall learn and remeber:

1.1,1.2 
- definition of a knot (polygon embedded in R3)
- elementary moves on polygonal curves
- "local" definition of equivalence of knots: a finite sequence of elementary moves
- orientation of a knot

1.3
- "global" definition of equivalence of knots: homeomorphism of R3 that transforms K1 into K2
(the proof is by methods of algebraic topology can be omitted)
- examples of homeomorphisms - rotation, translation, !! various kinds of twists (ex. 1.3.3) !!
- mirror image (plane reflection, which is orientation-reversing)
- R3 ---> S3 (1-point compactification)

1.4
- link = a finite collection of knots 
	- ordered (K1,...,Kn) vs. unordered (union of Ki) - makes a difference in equivalence, Murasugi chooses unordered
- equivalence of links (two versions)

1.5
- connected sum K1 # K2 (= gluing two knots together) 
	- TO DO: prove that it does not matter where you cut the knot !!
- knot decomposition into a onnected sum, indecomposable knots are called prime
- Theorem: every knot admits a unique decomposition to prime knots (omit the proof)
- (all knots, #) is a monoid --- TO DO: understand the proof !!

1.6
This section is about how to make # a group operation, by weakening the notion of equivalence into something called cobordism.
You can skip the section.