Here is a list of some introductory books on Stochastic partial differential equations.
For those which I have read, I have included some comments. You are welcome to send me more references to be included here.
Da Prato / Zabczyk: Stochastic equations in infinite dimensions.
(Encyclopedia of Mathematics and Its Applications, Vol. 44), Cambridge University
R. Carmona (Editor), B. L. Rozovskii (Editor): Stochastic Partial Differential Equations : Six Perspectives
( AMS Mathematical Surveys and Monographs, No. 64.)
(Mathematical Research, Vol 85), Akademie Verlag, 1995. Stochastic partial differential equations are studied using the infinite dimensional stochastic analysis, the theory of evolution operators and rigged Hilbert spaces. The authors consider existence and uniqueness theorems as well as possibilities of the approximation.
(London Mathematical Society Lecture Note, No 216), Cambridge Univ Press, 1995. ISBN: 0521483190.
Kluwer, 1998. ISBN: 0792349849.
Pitman Research Notes in Mathematics Series, No 268, 1992.
Proceedings of a conference held in Trento.
Centre de Mathématiques Appliquées
CNRS - Ecole Polytechnique
F-91128 Palaiseau, France.
Tel. 00 33 1 69 33 45 67 - Fax 00 33 1 69 33 30 11