One of my all time favorite female sleuths is Agatha Christie's Miss Jane Marple.
Back in the mid 80's, I had grown tired of historical romances and was in dire need of something else to read. While on vacation one year, a friend recommended the Golden Age mysteries. I'd never heard the term before and asked him to explain. He told me that during the 30's and 40's, there was an incredible amount of crime fiction written, with a murder or two at the center of every plot. The stories were constructed in such a way, that the reader would be hard pressed to figure out whodunit. He gave me the names of several authors I should check out - Dorothy L. Sayers, Margery Allingham and the brilliant Agatha Christie chief among them. I told him I had already read several Christie novels, and he pressed me to read them all. As it turns out, I still haven't done that (I still have several Hercule Poirot books left to read), but I have read all of the Miss Jane Marple novels and short stories I could get my hands on. Many of the short stories are within mystery anthologies, and it took me a while to track them all down, but once I had, I was delighted.
I believe one of the detectives in the stories says that Miss Marple has a mind like a steel trap. I agree. At first glance, nearly all of the people she encounters underestimate her. Who they see is a little old lady; a bit of a busy body, always knitting something, oblivious to the goings on about her, lost in her own little world. What they don't know is that behind that non threatening, demur and sometimes very absent minded exterior, is a woman who misses nothing. She is a crack observer of human nature and the evils we humans inflict upon each other.
The way she is able to piece together the most diverse threads of a murder mystery are nothing short of amazing. Shifting through clues of odd bits of conversation and seemingly unrelated events, she (with the help of the local police) zeroes in on the guilty party and always get her man, or woman.
One aspect of the stories which sets them apart are the various relatives, friends, relatives of friends, etc. which make up the vast array of people who populate her world. Miss Marple knows so many people, that wherever she goes, there is always be someone with whom she is acquainted.
If you haven't read any of the stories or novels, then may I make a suggestion? If possible, read them in sequence, or as close to it as you can. I say this because the time periods the stories are set in changes. For instance, many of the early novels take place in Miss Marple's home of St. Mary Mead. Later however, she begins to travel, and her world and the situations she is exposed to expand wonderfully.
One last thing. You may also enjoy the British films and television series. I certainly do. It's great fun to watch the novels unraveled on screen. The most recent incarnation of Miss Marple is wonderfully played by Geraldine McEwan (as seen above).