1 Index of notation and terms -- 2 Set theory, requirements, witnesses -- 3 What's new in this chapter? -- 4 Priorities (a splitting theorem) -- 5 Reductions, comparability (Kleene-Post Theorem) -- 6 Finite injury (Friedberg-Muchnik Theorem) -- 7 The Permanence Lemma -- 8 Permitting (Friedberg-Muchnik below C Theorem) -- 9 Length of agreement (Sacks Splitting Theorem) -- 10 Introduction to infinite injury -- 11 A tree of guesses (Weak Thickness Lemma) -- 12 An infinitely branching tree (Thickness Lemma) -- 13 True stages (another proof of the Thickness Lemma) -- 14 Joint custody (Minimal Pair Theorem) -- 15 Witness lists (Density Theorem) -- 16 The theme of this book: delaying tactics -- Appendix A: a pairing function -- Bibliograph -- Solutions to selected exercises.