The tools of mathematical statistics find wide application in climatological research. Indeed, climatology is, to a large degree, the study of the statistics of our climate. Mathematical statistics provides powerful tools which are invaluable for this pursuit. Applications range from simple uses of sampling distributions to provide estimates of the uncertainty of a climatological mean to sophisticated statistical methodologies that form the basis of diagnostic calculations designed to reveal the dynamics of the climate system. However, even the simplest of statistical tools has limitations and pitfalls that may cause the climatologist to draw false conclusions from valid data if the tools are used inappropriately and without a proper understanding of their conceptual foundations. The purpose of this book is to help the climatologist understand the basic precepts of the statistician's art and to provide some of the background needed to apply statistical methodology correctly and usefully. We do not claim that this volume is in any way an exhaustive or comprehensive guide to the use of statistics in climatology, nor do we claim that the methodology described here is a current reflection of the art of applied statistics as it is conducted by statisticians. Statistics as it is applied in climatology is far removed from the cutting edge of methodological development. This is partly because statistical research has not come yet to grips with many of the problems encountered by climatologists and partly because climatologists have not yet made very deep excursions into the world of mathematical statistics. Instead, this book presents a subjectively chosen discourse on the tools we have found useful in our own research on climate diagnostics.