  The Wheeler-DeWitt equation is solved for the Bergmann-Wagoner scalar-tensor
gravitational theory in the case of Friedmann-Robertson- Walker cosmological
model. We present solutions for several cosmological functions: i)
\lambda(\phi)=0, ii) \lambda(\phi)=3\Lambda_0\phi and iii) a more complex
\lambda(\phi), that depends on the choice of the coupling function, considering
closed, flat and hyperbolic Friedmann universes (k=1, 0, -1). In the first two
cases we show particular quantum wormhole solutions. Also, classical solutions
are considered for some scalar-tensor theories, and we study the third
quantization of some minisuperspace models.
