The Battle of Britain has been a very interesting subject for me. Can you suggest any books about it?
Sure; from the book list Stephen Bungay's The Most Dangerous Enemy: A History of the Battle of Britain is an excellent starting point, eminently readable and well researched, it would be my pick if you just go for one. For a slightly more concise read Richard Overy's The Battle of Britain: Myth and Reality packs a lot in to a fairly slim volume; for a more expansive version James Holland's The Battle of Britain: Five Months Which Changed History devotes a good chunk to the Battle of France as well. Wood & Dempster's The Narrow Margin: The Battle of Britain and the Rise of Air Power 1930-1949 is something of a classic, first published in 1961, but a little dated now compared to the previously mentioned books.
For a hugely comprehensive reference (with a price tag to match), The Battle of Britain - Then & Now from After The Battle press is the one, 800+ pages, 1,700 photographs, and comprehensive loss lists.
There's no shortage of individual pilot biographies and autobiographies as well; just to pick out a couple, Geoff Wellum's First Light and Tom Neil's Gun Button To Fire are fine examples from a Spitfire and Hurricane pilot respectively. To branch out a bit from books, the Imperial War Museum have also digitised huge numbers of audio interviews, including Battle of Britain pilots; they have a page with snippets from a number of them, linking through to the full things.