Who they were
Abbas I (1571–1629, r. 1588–1629) is generally regarded as the greatest of the Safavid shahs. He inherited a state losing territory to the Ottomans and the Uzbeks, and began by buying time with a humiliating peace.
What they did
Abbas rebuilt the army around ghulam slave-soldiers and artillery organized with English advice — the Sherley brothers’ role is often overstated — then retook Tabriz, Baghdad, and the lost provinces. He moved the capital to Isfahan in 1598 and rebuilt it as a planned imperial city, with the Naqsh-e Jahan square (now a UNESCO site), the Shah Mosque, bridges, and boulevards. He ran royal monopolies and the silk trade, settled Armenian merchants at New Julfa with wide privileges, concluded trade agreements with the English and Dutch East India companies, and took Hormuz from Portugal with English naval help in 1622. At home he maintained the Shia state while dealing pragmatically with Christian minorities.
Legacy
His reign was the Safavid apogee: Iran under Abbas was among the leading powers of its age. Yet a pathological fear of conspiracies led him to kill or blind his own sons, leaving only weak successors.