I am a big mystery fan.  I have started to read more fantasy and science fiction in an effort to expand my reading pleasure.  I was wondering if there is a book or books that exist that combines both mystery and science fiction or fantasy in them???

You may want to try the Thursday Next series by Jasper Fforde. The first in the series is called "The Eyre Affair." The main character is a Literary Detective trying to track down the villian who has found a way to steal characters out of novels.

Jim Butcher's Dresden series is good.  He is a private investigator who is a wizard.

A more scifi series is Glen  Cook's Garrett P. I. series.

If you really want a couple that are a bit more odd you can try Simon R Green's Tales from the Nightside series (but I will warn you it gets a bit bloody by the time you get to the 3rd or 4th book. Then there is S. Andrew Swann's 2 books Dragons of the Cuyahoga and Dwarves of Wiskey Island they are a bit of a mix of mystery scifi/fantasy and political.

and if you try and like Dresden there are some other fun similiar books. Dog Days by John Levitt  and Unshapely things and Unquiet Dreams by Mark Del Franco being three I personally enjoyed.

Thank you for the suggestions...Now I am off to see which ones are available to order.

Another thought might be Lois McMaster Bujold's Vorkosigan series.  It's sci-fi, and while he's not officially an investigator (well, actually he goes through a number of job titles) Miles Vorkosigan often finds himself having to solve crimes. 

Here's the weird thing about that series -- there are two possible proper places to start!  You can start with the two books about Miles' parents, Shards of Honor and Barrayar, which are sort of prequels to the series, or you can jump right into Miles' first book, The Warrior's Apprentice, which doesn't assume you've read the earlier books.

Issac Asimov has a classic sci-fi series featuring a police detective and his robotic partner -- starts with The Caves of Steel.

Also try The big over easy by Jasper Fforde, it is a Nursey Crimes series book. They are realllly funny and a nice who dun it.

I can recommend Down These Dark Spaceways, an anthology edited by Gardner Dozois.

Blurb found online ...

"They used to say it couldn’t be done, that no once could blend the mystery story with the science fiction story," says Mike Resnick in his introduction to Down these Dark Spaceways. He cites such great novels as Alfred Bester’s The Demolished Man and Isaac Asimov’s The Caves of Steel as examples that disproved this sentiment over fifty years ago. In this anthology made available through the Science Fiction Book Club, Resnick presents six novellas synthesizing these two literary genres. These are not in the vein of the classic British mystery or today’s "cozy" mystery; he uses the Black Mask school as his jumping-off point, with protagonists more in the style of Dashiell Hammett’s Sam Spade and Raymond Chandler’s Philip Marlowe than Arthur Conan Doyle’s Sherlock Holmes and Agatha Christie’s Hercule Poirot."

Also look for Liz Williams' series featuring Detective Inspector Chen--I've read the first one (Snake Agent) and really enjoyed it--a great blend of fantasy and detective fiction.

Cheryl

"Monument" by Lloyd Biggle, while not a mystery in the traditional sense, kept me guessing right to the end.

by Randall Garrett is a mystery set in an alternate universe where magic works just like science. There is a series of them featuring Garrett's creation Lord Darcy.

And of course, Asimov's robot mysteries featuring R. Daneel Olivaw and Lije Bailey, The Caves of Steel and The Naked Sun. 

Definitely check out Barry Hughart's Master Li series if you are looking for a mix of mystery and fantasy. The books are:

Bridge of Birds

The Story of the Stone

Eight Skilled Gentlemen

OR there is an omnibus called The Chronicles of Master Li and Number Ten Ox, but it costs over $100. There is a new printing coming out later this year, however, that only costs around $30.

I love Point of Hopes and Point of Dreams, written by Melissa Scott and Lisa A. Barnett. The main character is a "pointsman" (something like a police officer) in an alternative universe that's a version of late-Renaissance Europe in which Renaissance theories of astrology and magic actually work. The worldbuilding is meticulous, the characters are engaging, and the mystery plots are well done.

Also, Matthew Hughes has a series of novels about a character, Hengist Hapthorne, who's a "discriminator"--a sort of private investigator--in a far-future universe in which the balance between rationality and magic is shifting. I've only read one of these novels, Majestrum, but I liked it a lot.

Also Douglas Adams Dirk Gently's Holistic Detective Agency I think is the title. And although not exactly fantasy, ok pretty much not fantasy at all but a fantastic book is Tales of the Black Widowers by Iaasic Asimov.

Diane Tregarde Investigations by Mercedes Lackey. There are three books: Children of the Night, Burning Water, and Jinx High.

They're about a witch/Guardian who investigates paranormal mischief. She's a romance writer by day. Always loved these books! When they came out in a new edition I bought them again, even though I already had a set in paperback.

It's strange that the SF/mystery combo is so much more common than the fantasy/mystery combo. . .

Second the recommendations of Bujold and Asimov.

Sharon Shinn wrote a novel called Wrapt in Crystal that is a good SF/mystery, and adds a bit of romance and philosophy to the mix.

I'll second the reccomendation of Jim Butcher's Dresden Files. The first book is Storm Front. These are some seriously great books. A good mix of fantasy/mystery./action/humor.