As Elizabeth Peters, she has written the Amelia Peabody series, the Vicky Bliss series, and the Jacqueline Kirby series, as well as nine non-series mysteries. All of these books are injected with subtle humor that is a joy to read. Her characters are well developed and the subjects are well researched.
Amelia Peabody appears to be the dearest to Ms. Mertz's heart. No wonder! Amelia is a Victorian archeologist as well as an amateur detective and a feminist. Ironically, this series didn't start out as a series. The first book, Crocodile on the Sandbank, was written as a stand-alone mystery novel. The series is now up to twelve books with another book due out next spring/summer. The characters age as the series progresses thus allowing for superior character development. You will also get a nice feel for Egyptology in Victorian times. Don't be surprised if you suddenly develop an urge to read non-fiction books about Egyptology, Amelia B. Edwards, and other Egyptologists that revolve on the periphery of Amelia's world. Try to read this series in order.
Vicky Bliss is my favorite character. She is an art historian, somewhere in her late 20's/early 30's. She is blonde with a Playboy bunny figure and an intellectual mind. However, she has a bad habit of speaking and acting before she thinks. There are five books in this series with rumor that another one may be written within the next few years. Try to read these books in order. I also recommend that you read The Camelot Caper along with these books. (No, I'm not telling you the reason!)
Jacqueline Kirby is a librarian (at least, at the beginning of the series). I consider her ageless, though my guess is that she is in her late 30's or early 40's. She is the most independent of the three series characters. She also has a sparse history. This is another series that didn't start as a series. In fact, Jacqueline wasn't even the heroine in the first book, The Seventh Sinner. However, she was the most engaging of the characters and she was brought back as the protagonist in the next three books. The first book will seem rather dated but it does give you a good picture of Jacqueline's character. The best of the series (and the best of Elizabeth Peters, in my humble opinion) is Naked Once More. Ms. Mertz received the Agatha Award in 1989 for this book.