Lack of examples? What? Algebra is literally overflowing with examples. Algebraic structures generalize concrete structures you've probably already seen else

Lack of examples? What? Algebra is literally overflowing with examples. Algebraic structures generalize concrete structures you've probably already seen elsewhere in mathematics: from arithmetic, addition and multiplication, as the video explained, from discrete math, you can write down lots of interesting, finite examples, symmetry groups of geometric figures generate lots of interesting finite and infinite (Lie) groups, 1- and 2-dimensional wallpaper patterns are classic examples, etc, etc. In comparison, for example, it's quite non-trivial to describe a single interesting 4-manifold.