1 Introduction and motivation  
2 A brief introduction to classifier calibration  
2.1 Why calibration matters  
2.2 Common forms of miscalibration, and how to fix them  
2.3 Multiclass calibration  
3 From proper scoring rules to calibration  
3.1 Decompositions of proper scoring rules  
4 Evaluation and visualization of classifier calibration  
4.1 Visualizing calibration  
4.2 Evaluating calibration error: the binary case  
4.3 Classwise calibration error  
4.4 Confidence calibration error  
5 Calibration methods  
5.1 Preliminaries  
5.2 Two-Class Test Cases  
5.3 Calibration for Binary Classification  
5.4 Calibration for Multi-class Classification  
5.5 Extended methods for post-hoc classifier calibration  
5.6 Methods that can improve calibration during training time  
5.7 Methods for probability calibration for other predictive settings  
5.8 Methods designed for other research fields and applications  
6 Hypothesis tests for calibration  
7 Concluding remarks