1 Introduction.- 1.1 The Big Picture.- 1.2 Genesis.- 1.3 The Need for Progressive Censoring.- 1.4 A Relatively Unexplored Idea.- 1.5 Mathematical Notations.- 1.6 A Friendly Note.- 2 Mathematical Properties of Progressively Type-II Right Censored Order Statistics.- 2.1 General Continuous Distributions.- 2.1.1 Introduction.- 2.1.2 Results.- 2.2 The Exponential Distribution: Spacings.- 2.2.1 Introduction.- 2.2.2 Progressively Type-II Right Censored Spacings.-...