VSP, Utrecht, The Netherlands, 1994. Stimulated by internal demands of mathematics, in recent years integral geometry has gain a powerful impetus from computer tomography. Now integral geometry serves as the mathematical background for tomography which in turn provides most of the problems for the former. The book deals with integral geometry of symmetric tensor fields. This section of integral geometry can be viewed as mathematical basis for tomography of anisotropic media whose interaction with sounding radiation depends essentially on the direction in which the latter propagates