In this section we describe the basic theory underlying critical collapse of the type that forms arbitrarily small black holes (later called type II, see also Section 2.4). We begin with the mathematical origin of its three main characteristics, which were already summarised in the introduction:

- universality with respect to initial data;
- scale-invariance of the critical solution;
- black hole mass scaling.

2.1 Universality

2.2 Self-similarity

2.3 Mass scaling

2.4 Type I

2.5 Coordinate choices for the dynamical systems picture

2.6 Approximate self-similarity and universality classes

2.7 The analogy with critical phase transitions

2.2 Self-similarity

2.3 Mass scaling

2.4 Type I

2.5 Coordinate choices for the dynamical systems picture

2.6 Approximate self-similarity and universality classes

2.7 The analogy with critical phase transitions

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