This book selects excellent application questions from the national and provincial mathematics competition volumes in recent years, and is carefully designed and compiled according to the general rules, thinking methods, thinking strategies and various common types of problem solving. The selected cases are typical, exemplary, novel and contemporary. More importantly, the author's analysis of examples is thorough and simple, and attaches importance to embodying some model strategy or infiltrating some mathematical method or providing some conclusions; By grasping the key points, breaking through the difficulties, revealing the thinking process, and substituting the topic for the topic, readers can really draw inferences, optimize the structure of knowledge application, activate thinking, and get twice the result with half the effort, which is really conducive to the transformation of readers from "learning" to "learning"