While not specifically only about DNA, I recently read a very interesting book called "The Gene / An Intimate History" by Siddhartha Mukherjee.
The first 60% (maybe more) is a detailed history of the belief systems/ideas that lead to the progression of scientific research on genetics - starting from early religious ideas of inheritance, to Darwinism (theories of evolution, etc.), to the discovery of DNA, and many other historical events in between, to future things like encoding computer programs on DNA strands. The book is very interesting especially if you like to follow the logical progression of ideas, as people build on each others discoveries, to advance our knowledge and understanding of questions that seem very simple (like how can a child look a lot like both their parents?).