Retrograde analysis reads programs from the end to the beginning: treat statements as constraints on prior states, propagate sets of states backward, and compare the reachable inputs with the intended specification. This tutorial condenses a longer exposition to a focused guide with definitions, worked examples (toy branches, sorting networks, binary search), loop treatment via fixpoints, and a range-algebra appendix that standardizes array splits and midpoints. The aim is practical: short proofs, concrete invariants, and drop-in code and property tests