This Book Proposes A New Method For Analyzing The Extreme - Value Behaviour Of Random Fields And Represents An Original Contribution To Statistical Methodology For Extremes. The Author Is A Main Contributor To Research In This Field, And Has Based This Book On A Lecture Course That He Gives In Beijing. The Book Is Presented In Two Parts. The First Part Presents A General Method For Producing Asymptotic Expansion Of The Tail Probability Of Extremes In A Random Field. The Second Part Describes Five Relatively Complicated Applications Of The Technique In Problems That Emerge In Practical Situations. All The Examples Would Be Difficult To Analyze Using Classical Methods, And Yakirs Novel Technique Is Designed To Be More Easily Understandable To Specialists