Ancient to Classical : Iron Working, Metal Casting, Alphabet, Aesthetics, Monarchy, Code of Laws, Mathematics, Horseback Riding.
Classical to Medieval : Machinery, Feudalism, Philosophy, Theology, Civil Service, Music.
Medieval to Renaissance : Astronomy, Printing Press, Gunpowder, Education, Nationalism.
Renaissance to Industrial : Scientific Method, Steel, Steam Power.
Industrial to Modern : Refrigeration, Radio, Flight, Plastics, Rocketry, Ecology.
Modern to Future : Fusion, Genetics, Stealth.
Getting any one in each group advances to the new era.
Mind you, the only effects of entering a new era are (a) techs in the new era cost more, and (b) the music changes - except, alas, going from Modern to Future.