A fun read about the history of jigsaw puzzles is Anne Williams book Jigsaw Puzzles: Piecing Together a History.
To get a visual sense of how jigsaw puzzles have evolved, check out David Spearer's massive collection of photos of puzzles by different companies:
and Bob Armstrong's examples of different cutting styles in wood puzzles:
Photo of a wooden jigsaw puzzle from 1860. Photo borrowed from Bob Armstrong's website www.oldpuzzles.com.