the Second Age

The Second Age was also known as the Age of elves because elves were the numerically and politically dominant race. The period stretched from the end of the First Unmaking to the start of the Second Unmaking.  Depending on whom you ask, the First Age lasted anywhere between 2,000 years and 200,000 years.
Artifacts from the Second Age are fairly common but most are not that valuable.  Working tools and weapons of the Second are highly prized in the Third Age, as are intact written works.  Elven was the predominant but not the only language spoken and written during the Second Age.

The elves of the Second Age were fairly different from the surviving elves known in the The Third Age. They were closer to modern humans in their habits. They built castles, cities, farms, and mines quite similar to what the humans have now.
Most, but not all elven structures were ruined by the end of the Second Unmaking.  The plurality of the intact structures are in the modern Elven Empire.  Others became the basis for human cities and fortification in the Third Age.  Lots of human fortresses and cities were built partially from salvaged ruins of the Third Age.
Surviving maps indicate that there were roughly 30 to 40 elven nations at the peak of the Second Age.  The largest and most politically powerful nation at the time was Disteria, and the modern dark elves claim dissent from the ancient Disterians.  They named their nation Kahdisteria or "New Disteria." 
Most modern grey elves are descended from the Second Age nation of Lunatus.  Lunatus was one of the lesser national powers of the Second Age but due to its geography was the nation least damaged by the Second Unmaking.  Thus the grey elves claim to be the culturally purest elves alive today.  The modern wood of @[Codenya do not focus heavily on their Second Age ancestors.  They claim their ancestors were a mix of refugees from a great many elven nations.