1 Introduction.- 1.1 Derivatives of Random Variables.- 1.2 Infinitesimal Perturbation Analysis.- 1.3 The Role of Representations.- 1.4 Basic Theoretical Tools.- 1.5 Derivatives of Measures.- 1.6 A Simple Illustrative Example.- 1.7 Two Views of Conditioning.- 1.8 A Brief Perturbation Analysis Lexicon.- 1.9 Summary.- 2 Three Extended Examples.- 2.1 Renewal Process.- 2.2 Single-Server Queue.- 2.3 (s, S) Inventory System.- 2.4 Summary.- 3 Conditional Monte Carlo Gradient Estimation.- 3.1 The GSMP Framework.- 3.2 Infinitesimal Perturbation Analysis.- 3.3 Gradient Estimation via Conditioning.- 3.4 Discontinuous Performance Measures.- 3.5 Other Stopping Times.- 3.6 Long-Run Average Performance Measures.- 3.7 Higher Order Derivative Estimators.- 4 Links to Other Settings.- 4.1 Special Cases.- 4.2 An Alternative Characterization.- 4.3 Likelihood Ratio Method.- 4.4 Rare Perturbation Analysis.- 4.5 Weak Derivatives.- 4.6 Discontinuous Perturbation Analysis.- 4.7 Augmented Infinitesimal Perturbation Analysis.- 4.8 Likelihood Ratio Method via Conditioning.- 5 Synopsis and Preview.- 5.1 Summary of Main Results.- 5.2 Efficient Implementation.- 5.3 Gradient-Based Optimization.- 5.4 Preview of Applications.- 6 Queueing Systems.- 6.1 Single Queue Notation.- 6.2 Timing Parameters.- 6.3 Discontinuous Performance Measures.- 6.4 Finite Capacity Queue.- 6.5 Priority Queue.- 6.6 Multiple Servers Second Derivative.- 6.7 Multiple Non-Identical Servers.- 6.8 The Routing Problem.- 6.9 Other Threshold-Based Parameters.- 6.10 An Optimization Example.- 6.11 Multi-Class Queueing Network.- 7 (s, S) Inventory Systems.- 7.1 Standard Periodic Review Model.- 7.2 Service Level Performance Measures.- 7.3 Hybrid Periodic Review Model.- 8 Other Applications.- 8.1 A Component Replacement Problem.- 8.2 Pricing of Financial Derivatives.- 8.3 Design of Control Charts.- References.