Short answers, pulled from the story.
The primary structural materials were stone, wood, marble, and concrete. Pozzolana mortar, made from volcanic clay found around Naples mixed with lime, was especially significant because it could set underwater and cure as hard as natural rock. A variant using crushed brick dust rather than volcanic ash was used in the Hagia Sophia and achieved a tensile strength of 500 psi.
Roman aqueducts moved water entirely by gravity through slightly slanted stone channels drawn from mountain springs. The eleven aqueducts supplying Rome had a combined length of 350 km and delivered more than one million cubic metres of water per day, enough for 3.5 million people. Where depressions deeper than 50 metres had to be crossed, engineers used inverted siphons to push water uphill.
Romans used human muscle, animal power, water wheels, wind-powered sails, and passive solar heat. Water wheels served primarily to grind grain and raise water, and evidence exists that they also powered stone-cutting saws. Steam power remained theoretical; Hero of Alexandria published schematics for a rotating steam device producing roughly 1,500 rpm, but it was never practical at industrial scale.
Rome developed the pilum javelin, designed to be destroyed on first use to prevent enemies from reusing it, and the lorica segmentata segmented plate armor. The Romans were probably the first to mount ballistas on wheeled carts for battlefield mobility. They also invented the corvus boarding bridge during the First Punic War and used the testudo shield-wall formation for protection under projectile fire.
Roman physicians created or pioneered hemostatic tourniquets, arterial surgical clamps, and various surgical instruments still recognizable today. The Roman army established the first known dedicated battlefield surgery unit. Dental fillings were first mentioned by Cornelius Celsus in the 1st century AD, and iron tooth implants have been found in archaeological evidence from Gaul.
Technical knowledge in Rome was passed privately from master tradesmen to apprentices and rarely published; only a few writers such as Vitruvius, Pliny the Elder, and Frontinus documented methods in detail. The turbulence of Late Antiquity and the early Middle Ages interrupted these transmission chains. Some advances, including those in civil engineering and the mechanical reaper, were not matched again until the 19th century.