April of Bookspot Central and Dragon Ashes calls this book a fantasy of manners and the phrase is quite apt. Brennan evokes the society, conventions, and scientific knowledge of the Victorian era, an era not conducive to strong- and scientific-minded women. The book is written as a memoir detailing both the character's life and the results of her research.
There's a lot to like about this book. The book and characters are well written. Those who don't mind a different style of format or plot will enjoy this. An extra benefit is interior artwork that livens up the reading experience.
The book's drawbacks are fairly minor. Like a 19th Century treatise, the memoir is a little dry, a little too linear, so the story might have been stronger with some more personal feeling by the narrator. Also, towards the end, the plot becomes a little too much like an Indiana Jones-style caper.
There was also little of dragons in this book actually, but the preface reveals that it's the first of a series so perhaps that's to be expected.
A Natural History of Dragons was a very solid and enjoyable book and I plan to pick up the next one in the series.