The Three-Body Problem is a science fiction novel by Chinese writer Liu Cixin. It is the first part of the Remembrance of Earth's Past, a science fiction trilogy, and is the first work of Chinese science fiction to be translated into English. The Three-Body Problem was released in 2008 and won the Hugo Award for Best Novel in 2015.
The trilogy is now complete. The second part of the trilogy is entitled The Dark Forest and was released in 2008. Liu Cixin released the third and final installment, Death's End, in 2010. The novel is considered one of the greatest works of science fiction of all time and has been hailed as a classic.
So to answer your question, yes, The Three-Body Problem is finished. Liu Cixin completed the trilogy with the publication of Death's End in 2010. It is a fantastic and suspenseful ride, and if you enjoy epic science fiction, you should definitely read it!