The origin of this book lies in an invitation to give a series of lectures on

Malliavin calculus at the Probability Seminar of Venezuela, in April 1985.

The contents of these lectures were published in Spanish in [176]. Later

these notes were completed and improved in two courses on Malliavin calculus

given at the University of California at Irvine in 1986 and at Ecole

Polytechnique Federale de Lausanne in 1989. The contents of these courses

correspond to the material presented in Chapters 1 and 2 of this book.

Chapter 3 deals with the anticipating stochastic calculus and it was developed

from our collaboration with Moshe Zakai and Etienne Pardoux.

The series of lectures given at the Eighth Chilean Winter School in Probability

and Statistics, at Santiago de Chile, in July 1989, allowed us to

write a pedagogical approach to the anticipating calculus which is the basis

of Chapter 3. Chapter 4 deals with the nonlinear transformations of the

Wiener measure and their applications to the study of the Markov property

for solutions to stochastic differential equations with boundary conditions.

The presentation of this chapter was inspired by the lectures given at the

Fourth Workshop on Stochastic Analysis in Oslo, in July 1992. I take the

opportunity to thank these institutions for their hospitality, and in particular

I would like to thank Enrique Cabana, Mario Wschebor, Joaquin

Ortega, Siileyman Ustiinel, Bernt 0ksendal, Renzo Cairoli, Rene Carmona,

and Rolando Rebolledo for their invitations to lecture on these topics.