A very hands-on approach to Coxeter systems.
Video 2:    • The Coxeter Classification 2/2: Who c...  
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00:00 Opening
02:23 Part 1: Introducing Coxeter systems
10:14 Part 2: Proving things are infinite
15:23 Part 3: Symmetry groups of polyhedra
25:00 Part 4: The exceptional systems
32:18 Conclusion

Some casual overviews of finite groups, if you want a primer for this video:
From 3Blue1Brown –    • Group theory, abstraction, and the 19...  
From Numberphile –    • Monster Group (John Conway) - Numberp...  

If you're looking for more detailed proofs of results like the Word Property, I recommend the textbook Combinatorics of Coxeter Groups by Björner and Brenti which covers these in the first 3 chapters.

Small corrections thanks to commentors:
*The word 'prism' at 19:16 should be 'pyramid', or equivalently an asymmetric prism so that reflecting through the length is not a symmetry.