"HILBERT's TENTH PROBLEM"
a book written by Yuri
MATIYASEVICH
Russian original:  
English translation:  
Hilbert's Tenth Problem  
The MIT Press, Cambridge, London, 1993  
The Publisher's page of the book  
Traduction française:  
Le dixième problème de Hilbert.
Son indécidabilité 

MASSON Editeur, Paris, 1995  
The tenth Problem is one of the 23 problems posed by David
Hilbert in his famous lecture "Mathematical
Problems". The 10th problem is about Diophantine
equations.
STATEMENT OF THE PROBLEM  

IN DEUTSCH  IN ENGLISH  EN FRANÇAIS  HA PYCCKOM 
You can find more information connected with the problem, including updated bibliography, on the WWW site, devoted to Hilbert's tenth problem
You can get an impression of the book from the following documents available via WWW: