As a young reader, I read all the Nancy Drew books. The schoolgirl detective set me onto the path of becoming a lifelong crime fiction reader. Later I encountered Agatha Christie’s Miss Marple. A more recent favourite has been Lisbeth Salander, Stieg Larsson’s creation in The Millennium Trilogy. And I can’t forget Precious Ramotswe, the protagonist in the series The No. 1 Ladies’ Detective Agency by Alexander McCall Smith, or Temperance Daesee Brennan, the forensic anthropologist in the novels of Kathy Reichs.
Wikipedia has an extensive list of fictional female investigators from novels, short stories, radio, television, films and video games: https://en.wikipedia.org/wiki/List_of_female_detective_characters.Female detectives in fiction often contend with sexism, in addition to battling the mysteries at the centre of their cases. I just finished a novel, Murder Below Zero by John Lawrence Reynolds, in which the protagonist, Maxine Benson, is a police chief but many doubt her ability to handle policing because she is a woman. (My review of this book will be posted on September 8.)
The Guardian newspaper recently had an article about female detectives in literature: https://www.theguardian.com/books/2017/jul/26/top-10-female-detectives-in-fiction?CMP=twt_books_b-gdnbooks.
http://www.wonderslist.com/10-female-detectives-in-literature/ has another list.
A book that I think I’ll pick up is Pistols and Petticoats: 175 Years of Lady Detectives in Fact and Fiction by Erika Janik. I read an excerpt from the book and it sounds really interesting: http://lithub.com/women-detectives-in-fact-and-fiction/.