There are a number of contenders for the title of "first printed book in the world." The answer to this question is actually quite tricky because it depends on what one means by "printing" as well as "book." Historical evidence strongly suggests that the identity of the first book in print will probably never be known, because it's unlikely that it survived to the present day. There is also a great deal of cultural bias in the answer to this question, as some authorities commonly cite Western texts such as the Gutenberg Bible, while other experts contend that Asia would be the most likely point of origin.
Defining the Question
When determining the identity of the first printed book, it's important to define "printing." The simple transfer of words or symbols to paper, clay, fabric, and other materials is thousands of years old, and could be termed a form of printing. Many people define printing, however, as a much more recent mass production process using plates, blocks, movable type, or other media, which can be used to transfer ink to a surface over and over again, mechanizing the process and resulting in large numbers of copies. It is also important to note that many early printed books were not entirely printed, with most being illuminated and rubricated — decorated and having red text added — by hand after the printing process was finished.
Beyond that, others will argue over the definition of the word "book." Must it consist of multiple pages bound to a cover and spine, like a modern book, or might a scroll or a series of etched tablets be eligible? There is not really a right or wrong answer to this question. Perhaps a more practical approach would be to consider the length of the volume in question, since most would consider a book to be of more substantial length than, for example, a proclamation or a letter.
If woodblock printing is included, then a Chinese translation of the Diamond Sutra is the oldest known surviving example of a printed book. Woodblock printing is an ancient process that requires laboriously hand carving a wood block for every page of the book. A copy of this book in the British Library dates to the year 868 CE. There's a catch, however; other block printed editions are probably older, but are undated, making the Diamond Sutra the first printed book with a verifiable date, not the oldest printed book and most certainly not the first. The earliest examples of woodblock printing are estimated to date as far back as 220 CE.
Movable Type Printing
Some people prefer to use movable type as the distinction when dating the first printed book, arguing that the development of movable type was a huge leap forward in printing technology that revolutionized the ability to mass produce books. With movable type, each letter or character is separate, allowing the printer to set the type in lines or pages, print the material, and then break the type down and reuse it. With a set of movable type, the need to hand carve wooden blocks is eliminated, and it's possible to print much more quickly.
Evidence suggests that ceramic movable type was invented in China by Bi Sheng around the year 1040. Unfortunately, no surviving printed books from this period have been found. It's fairly clear that if the Chinese invented movable type, however, they were probably putting it to practical use. This means that the oldest printed book is likely a Buddhist religious text from the 11th century, even if researchers don't know which one. Sheng's type did not hold up well, according to contemporaries, and the concept was abandoned, with the Chinese returning to woodblock printing.
In Korea, someone took note of the Chinese explorations into movable type, and developed metalloid type at around the same time. Researchers believe that the Koreans were printing books with movable type as early as the 1200s, with the first surviving printed volume with metalloid type being the Jikji, which was printed in the year 1377. That's over 70 years before Johannes Gutenberg succeeded in printing his famous Bible in 1455 in Germany. Gutenberg is traditionally credited with inventing this printing method.
Learning from this Debate
The true identity of the first printed book may never be known unless researchers discover a well-preserved copy with an attached discussion of the date and printing techniques. It is interesting, nonetheless, to explore the history of printing and its impact on the world. It is also revealing to observe the history of crediting things invented in the East to developers in the West; in the case of printing, it is entirely possible that Gutenberg came up with the idea of movable type independently, which means that the Chinese and Gutenberg both deserve credit for inventing it. It is also possible that Gutenberg heard about Chinese and Korean experiments with movable type and decided to try it out for himself.