The Wind-Up Bird Chronicle by Haruki Murakami
I had heard a lot about Murakami so I finally decided to see what all the fuss was about. He is perhaps the most well-known modern Japanese author and his name often appears in the same sentence as "Magical Realism" and/or "Kafkaesque". Rightfully so. The Wind-Up Bird Chronicle is one of the most bizarre books I've ever read.
On the surface, the premise is simple. A young man who recently left his job searches for his missing cat. His search quickly takes a turn for the strange and he meets a colorful cast of characters including a female mystic obsessed with water, a World War II veteran who survived an unbelievable mission in Mongolia, and a high school girl with a scar and a morbid fascination. Along the way, the protagonist reflects on his married life and delves deep into his relationship with his wife and her enigmatic brother.
One of the reviews on the book used the word "Dreamlike" and that is the best word I can think of to describe The Wind-Up Bird Chronicle. If you're a fan of mystery, the fantastical, and you like the strange intertwined with the mundane, this is the book for you.