What is Abstract Algebra? - Group Theory and the 196,883-Dimensional "Monster"

References: Abstract Algebra - Wikipedia https://en.wikipedia.org/wiki/Abstract_algebra “Group theory, abstraction, and the 196,883-dimensional monster” - 3Blue1Brown https://www.youtube.com/watch?v=mH0oCDa74tE Axiomatic System - Wikipedia https://en.wikipedia.org/wiki/Axiomatic_system Axiom - Wikipedia https://en.wikipedia.org/wiki/Axiom Pure Mathematics - Wikipedia https://en.wikipedia.org/wiki/Pure_mathematics Group Theory - Wikipedia https://en.wikipedia.org/wiki/Group_theory Group (Algebra) - Wikipedia https://en.wikipedia.org/wiki/Group_(mathematics) Main Classes of Groups in Group Theory - Wikipedia https://en.wikipedia.org/wiki/Group_theory#Main_classes_of_groups Classification of Finite Simple Groups - Wikipedia https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups Finite Group - Wikipedia https://en.wikipedia.org/wiki/Finite_group Lie-Type Group - Wolfram Mathworld https://mathworld.wolfram.com/Lie-TypeGroup.html Monster Group - Wikipedia https://en.wikipedia.org/wiki/Monster_group Monstrous Moonshine - Wikipedia https://en.wikipedia.org/wiki/Monstrous_moonshine J-invariant and Q-expansion - Wikipedia https://en.wikipedia.org/wiki/J-invariant#The_q-expansion_and_moonshine Continuous Symmetry - Wikipedia https://en.wikipedia.org/wiki/Continuous_symmetry Geometric Group Theory - Wikipedia https://en.wikipedia.org/wiki/Geometric_group_theory