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The paper reviews the most important achievements in the study of the surface-reconstruction phase transition on the low-index single crystals of Pt, Ir, and Au. A number of methods very sensitive to the surface layers are used to study the stable and metastable structures of the (100), (110), and (111) faces. Detailed consideration of the kinetics, critical parameters, activation energy, and geometrical models for 2D-surface phase transitions are presented. Main theoretical results based on the Ising 2D-model, calculations of the free energy with an embedded-atom method, and equilibrium Monte Carlo simulations are also given.