Introduction -- Preliminary Remarks -- Why Random Fields? -- Notation and Definitions -- Noise and Errors -- Spatial Data and Basic Processing Procedures -- A Personal Selection of Relevant Books -- Trend Models and Estimation -- Empirical Trend Estimation -- Regression Analysis -- Global Trend Models -- Local Trend Models -- Trend Estimation based on Physical Information -- Trend Based on the Laplace Equation -- Basic Notions of Random Fields -- Introduction -- Single-Point Description -- Stationarity and Statistical Homogeneity -- Variogram versus Covariance -- Permissibility of Covariance Functions -- Permissibility of Variogram Functions -- Additional Topics of Random Field Modeling -- Ergodicity -- Statistical Isotropy -- Anisotropy -- Anisotropic Spectral Densities -- Multipoint Description of Random Fields -- Geometric Properties of Random Fields -- Local Properties -- Covariance Hessian Identity and Geometric Anisotropy -- Spectral Moments -- Length Scales of Random Fields -- Fractal Dimension -- Long-Range Dependence -- Intrinsic Random Fields -- Fractional Brownian Motion -- Classification of Random Fields -- Gaussian Random Fields -- Multivariate Normal Distribution -- Field Integral Formulation -- Useful Properties of Gaussian Random Fields -- Perturbation Theory for Non-Gaussian Probability Densities -- Non-stationary Covariance Functions -- Further Reading -- Random Fields based on Local Interactions -- Spartan Spatial Random Fields -- Two-point Functions and Realizations -- Statistical and Geometric Properties -- Bessel-Lommel Covariance Functions -- Lattice Representations of Spartan Random Fields -- Introduction to Gauss-Markov Random Fields -- From Spartan Random Fields to Gauss-Markov Random Fields -- Lattice Spectral Density -- SSRF Lattice Moments -- SSRF Inverse Covariance Operator on Lattices -- Spartan Random Fields and Langevin Equations -- Introduction to Stochastic Differential Equations -- Classical Harmonic Oscillator -- Stochastic Partial Differential Equations -- Spartan Random Fields and Stochastic Partial Differential Equations -- Covariance and Green's functions -- Whittle-Matérn Stochastic Partial Differential Equation -- Diversion in Time Series -- Spatial Prediction Fundamentals -- General Principles of Linear Prediction -- Deterministic Interpolation -- Stochastic Methods -- Simple Kriging -- Ordinary Kriging -- Properties of the Kriging Predictor -- Topics Related to the Application of Kriging -- Evaluating Model Performance -- More on Spatial Prediction -- Linear Generalizations of Kriging -- Nonlinear Extensions of Kriging -- Connections with Gaussian Process Regression -- Bayesian Kriging -- Continuum Formulation of Linear Prediction -- The "Local-Interaction" Approach -- Big Spatial Data -- Basic Concepts and Methods of Estimation -- Estimator Properties -- Estimating the Mean with Ordinary Kriging -- Variogram Estimation -- Maximum Likelihood Estimation -- Cross Validation -- More on Estimation -- The Method of Normalized Correlations -- The Method of Maximum Entropy -- Stochastic Local Interactions -- Measuring Ergodicity -- Beyond the Gaussian Models -- Trans-Gaussian Random Fields -- Gaussian Anamorphosis -- Tukey g-h Random Fields -- Transformations based on Kappa Exponentials -- Hermite Polynomials -- Multivariate Student's t-distribution -- Copula Models -- The Replica Method -- Binary Random Fields -- The Indicator Random Field -- Ising Model -- Generalized Linear Models -- Simulations -- Introduction -- Covariance Matrix Factorization -- Spectral Simulation Methods -- Fast-Fourier-Transform Simulation -- Randomized Spectral Sampling -- Conditional Simulation based on Polarization Method -- Conditional Simulation based on Covariance Matrix Factorization -- Monte Carlo Methods -- Sequential Simulation of Random Fields -- Simulated Annealing -- Karhunen-Loève Expansion -- Karhunen-Loève Expansion of Spartan Random Fields -- Epilogue -- A Jacobi's Transformation Theorems -- B Tables of SSRF Properties -- C Linear Algebra Facts -- D Kolmogorov-Smirnov Test -- Glossary -- References -- Index.