We (DH and I) both finished the 3 published Temeraire books. The books are set in Napoleonic times. I need to get some good references for that time period, since my knowledge of the history of the continent in that time period is sketchy at best. Yes, I do know that the books are Alternate History/Universe with the dragons, but I do like to be able to compare and contrast the alternate to the actual, if only in my own mind.
As I said, the books are set in Napoleonic times, with the addition of Dragon Aerial corps for the different nations. The Dragon Corps for England are a set apart and looked own upon service. Our Hero, Naval Captain William Laurence is serving at sea, captain of a ship that captures a French ship with a dragon egg aboard. The egg hatches while they are still at sea, and the Dragon corp folks are not available to see about harnessing the hatchling. The young officer whose lot is drawn is not accepted by the young dragon, but our captain, Will Laurence is. So our hero loses his ship and gains a dragon, to his initial displeasure.
Aerial battles, naval battles, trips to China, desperate flights back via Istanbul, hob nobbing with various folks of all ranks, and heroic fights and strategic retreats are all part of the books. They are fast reads so go for it!