In this book, the author has given some introduction to the nature of complexities and processes within Earth Sciences and some of theses are modeled through probabilistic and statistical methods using linear process. These are best exemplified through the use of axiomatic probability using univariate statistical methodology for scalar random variables and multivariate statistical methods for vector random variables. Several real geological examples are included in this book, which have been solved or partially solved to exemplify applications for solutions of specific earth science problems. The aim of these examples is to help the student to conceptually appreciate the problem and realistically formulate a simple mathematical model for its solution. In addition, several exercises are given at the end of each chapter so that the student can independently solve some advanced problems. This book will also be useful to professional Earth Scientists in formulating models and using statistical methods to make appropriate decisions in their chosen fields.