This monograph, "Interpolation of Spatial Data: Some Theory for Kriging," by Michael L. Stein, provides a mathematical treatment of kriging, a popular method for interpolating spatial data. Kriging is a special case of optimal linear prediction applied to random fields, but it often relies on estimating the covariance structure of the random field, which can introduce uncertainty. The author aims to develop the mathematical tools necessary to understand and address this uncertainty, particularly when the covariance structure is partially unknown. The book covers topics such as linear prediction, properties of random fields, asymptotic properties of linear predictors, and the equivalence of Gaussian measures. It includes new results and numerical studies, and offers practical suggestions for using kriging. The author also critically examines common practices in kriging, such as the use of certain classes of semivariogram models and the implications of measurement errors. The book is intended for researchers and practitioners interested in the mathematical and practical aspects of kriging.This monograph, "Interpolation of Spatial Data: Some Theory for Kriging," by Michael L. Stein, provides a mathematical treatment of kriging, a popular method for interpolating spatial data. Kriging is a special case of optimal linear prediction applied to random fields, but it often relies on estimating the covariance structure of the random field, which can introduce uncertainty. The author aims to develop the mathematical tools necessary to understand and address this uncertainty, particularly when the covariance structure is partially unknown. The book covers topics such as linear prediction, properties of random fields, asymptotic properties of linear predictors, and the equivalence of Gaussian measures. It includes new results and numerical studies, and offers practical suggestions for using kriging. The author also critically examines common practices in kriging, such as the use of certain classes of semivariogram models and the implications of measurement errors. The book is intended for researchers and practitioners interested in the mathematical and practical aspects of kriging.