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To learn about ancient science, the very best places to start are these:
Science Education in the Early Roman Empire
Greek Science
The Forgotten Revolution: How Science Was Born in 300 BC and Why it Had to Be Reborn
Early Greek Science: Thales to Aristotle
Greek Science After Aristotle
Ancient Science Through the Golden Age of Greece
Hellenistic Science and Culture in the Last Three Centuries B.C.
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For specific sciences, Routledge has an excellent Sciences in Antiquity Series, which so far includes:
Ancient Mathematics
Ancient Medicine
Ancient Botany
Ancient Natural History
Ancient Meteorology
Ancient Astrology
Time in Antiquity
Cosmology in Antiquity
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And for other exciting angles to pursue, these are all fascinating or useful:
Decoding the Heavens: Solving the Mystery of the World’s First Computer
Aetna and the Moon: Explaining Nature in Ancient Greece and Rome
The Prince of Medicine: Galen in the Roman Empire
Technology and Culture in Greek and Roman Antiquity
What Did the Romans Know? An Inquiry into Science and Worldmaking
The Oxford Handbook of Engineering and Technology in the Classical World
Greek Science of the Hellenistic Era: A Sourcebook
The Science of Harmonics in Classical Greece
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I also have recommendations for understanding the Origins of Christianity and Modern Philosophy.
