I think G.K. Chesterton explains his book rather well in his introduction, but it might help to start with a sense of the time in question. Chesterton started work on Eugenics and Other Evils in about 1910, but it was not completed and published until 1922. In his own introduction he talks about the period before and after "The War." The war he refers to is now called World War One.
We now have a distaste for the word Eugenics, largely driven by events in World War Two. But at the time this book was published, Eugenics was lauded to the skies as a wonderful idea, and Chesterton was nearly the only person saying in writing that Eugenics was in fact evil. A case could be made, and has been made, that today, though the word Eugenics is avoided, some practices that are in fact Eugenic practices, and some sciences that are in fact Eugenic sciences, enjoy great popularity and engender great public enthusiasm. To which practices and which sciences I refer, is left as an exercise for the reader.
"Though most of the conclusions, especially towards the end, are conceived with reference to recent events, the actual bulk of preliminary notes about the science of Eugenics were written before the war. It was a time when this theme was the topic of the hour; when eugenic babies (not visibly very distinguishable from other babies) sprawled all over the illustrated papers; when the evolutionary fancy of Nietzsche was the new cry among the intellectuals; and when Mr. Bernard Shaw and others were considering the idea that to breed a man like a cart-horse was the true way to attain that higher civilisation, of intellectual magnanimity and sympathetic insight, which may be found in cart-horses. It may therefore appear that I took the opinion too controversially, and it seems to me that I sometimes took it too seriously. But the criticism of Eugenics soon expanded of itself into a more general criticism of a modern craze for scientific officialism and strict social organisation."
The book is still controversial, and many people with many different political agendas point to "Eugenics" as backing up whatever claims they make. In any case, a remarkable number of comments and observations by Chesterton, on a wide variety of topics, could have been written last week. It was worth producing, and I think you'll find it worth reading.