This book has never been published before, although its contents have provided the basis for hundreds of papers, theses, and books on geostatistics. The chapters are based on the lectures of a summer course given by Georges Matheron in 1970; initially written in French, they were translated into English by Charles Huijbregts. They do not contain mathematical technicalities or practical case studies; instead, they present major topics like estimation variances, kriging systems, mining estimation, and intrinsic theory, all of which are established by simple proofs. The reader is invited to wonder about the physical meaning of the notions Matheron deals with. When Matheron wrote these lectures, he considered the theory of linear geostatistics complete; however, what was an ending for Matheron has been the starting point for most geostatisticians. Many discovered the book’s content indirectly, via the many borrowings one can find in several books; in such a situation, it is always instructive to come back to the original document, where the author's motivations, his physical intuitions, and his thoughts on the meaning of what he does are detailed. The decision to publish this book was motivated by the desire to introduce Matheron’s work to a larger audience. The book has remained faithful to the original notes while introducing a common structure for the chapters and sections, numbering equations sequentially within each chapter, numbering the figures (most of which were redrawn) sequentially, and adding captions. In addition, Matheron’s comments on the exercises, or suggestions for solutions, have been added.