There’s a bunch of them, depending on the culture you’re considering.

Old Babylonian period in mathematics, early second millennium BCE. Development of base-60 place-value number system and computation into advanced algorithmic system for solving a wide variety of mensuration, geometry, and what we would call algebra problems.

Late Babylonian period in astronomy, late first millennium BCE. Invention of sophisticated predictive mathematical astronomy using hundreds of years’ worth of recorded observations, periodic algorithms for predicting eclipses and other celestial phenomena, development of prototype of 360-degree circle* and coordinate systems for celestial position measurement, etc. Also included invention of horoscopic astrology, which nowadays we might not consider a scientific achievement but which was a HUGE driver and support system for the practice of quantitative science throughout several linked Eurasian civilizations for the next two thousand years.

Hellenistic period in Greek science, about 350 BCE-200 CE. Combined some Babylonian and Egyptian disciplines with Hellenic philosophical inquiries in a sustained burst of amazing scientific productivity. Galen, Euclid, Archimedes, Eratosthenes, Heron of Alexandria, Ptolemy, dozens of others, need I say more?

Gupta Era in India, early/middle first millennium CE. Included sophisticated mathematics such as algebra of signed quantities based on decimal place-value number system, plane trigonometry of sines and mathematics of transfinite quantities, ingenious computational methods in astronomy, developments in medicine and surgery, the expansion of rigorous theories of grammar that inspired the development of modern phonetics and linquistics by 19th-century Western Indologists, and many others.

Islamic Golden Age or Islamic Renaissance, about 9th-13th centuries CE. Immense multicultural scientific synthesis on a scale unsurpassed till the European Renaissance, building on Hellenistic and Indian mathematics, astronomy, medicine, philosophy and other disciplines. Major state-funded scientific research and engineering projects including the building of observatories and the establishment of teaching hospitals and institutions that became the prototypes of the medieval universities. Names like al-Khwarizmi, ibn al-Haytham, al-Biruni, Nasir al-Din al-Tusi, ibn Sina, a whole bunch of superstars who made crucial contributions in science and technology.

Twelfth-century Renaissance in the Latin West, early second millennium CE. Translations of Islamic scientific texts, integration of Islamic and classical learning with medieval Western philosophy, emergence of the great European universities. Roger Bacon, William of Ockham, Buridan, Oresme, you get the picture.

Renaissance, Scientific Revolution, Industrial Revolution, mid- to late second millennium CE in Europe: these are better known and you can find abundant information about them. But they were by no means the first periods of significant development in science.

Oh, and I left out ancient Egypt, other epochs in India, and China entirely, but there was a lot going on there that would make it into any reasonably comprehensive list of important ages of science. Unfortunately, I don’t know of any good introductory but comprehensive overview of the history of science as a whole in the great literate civilizations from earliest antiquity to the modern period, but somebody really should write one.

- Huh, I’m reminded that that was the first subject I ever posted to the SDMB about.
*Ou sont les neiges d’antan?..*