Content: Covariances and Associated Reproducing Kernel Hilbert Spaces Covariances and Negative Definite Functions Reproducing Kernel Hilbert Space Gaussian Random Fields Gaussian Random Variable Gaussian Spaces Stochastic Integral Representation Chaos Expansion Stochastic Integration for Gaussian Random Fields Multiple Stochastic Integrals Skorokhod Integral Skorokhod Differentiation Ogawa Integral Appendix Skorokhod and Malliavin Derivatives for Gaussian Random Fields Malliavin Derivative Duality of the Skorokhod Integral and Derivative Duration in Stochastic Setting Special Structure of Covariance and Ito Formula Filtering with General Gaussian Noise Bayes Formula Zakai Equation Kalman Filtering for Fractional Brownian Motion Noise Equivalence and Singularity General Problem Equivalence and Singularity of Measures Generated by Gaussian Processes Conditions for Equivalence: Special Cases Prediction or Kriging Absolute Continuity of Gaussian Measures under Translations Markov Property of Gaussian Fields Linear Functionals on the Space of Radon Signed Measures Analytic Conditions for Markov Property of a Measure-Indexed Gaussian Random Field Markov Property of Measure-Indexed Gaussian Random Fields Associated with Dirichlet Forms Appendix A: Dirichlet Forms, Capacity, and Quasi-Continuity Appendix B: Balayage Measure Appendix C: Example Markov Property of Gaussian Fields and Dirichlet Forms Markov Property for Ordinary Gaussian Random Fields Gaussian Markov Fields and Dirichlet Forms Bibliography Index