The vases (lekythoi) stored olive oil for the ritual anointing of the dead(every year), more specifically unmarried men

there are lots of different types,

Amphora-common type of handled vase, various sizes. wine/oil storage vessels.

Dinosa- no handles, rounded bottom.

Hydria- handled water vessel.

Kantharos- large ornate handled drinking vessel.

Krater- mixing jar for wine and water

Kylix- shallow drinking cup

Phiale- libation bowl, no handles or stem.

Pyxis- more like a box than a vase, but painted in the same style as the ones above.

Stamnos- type of amphora

Psykter- wide bottom cooling vase.

Oinochoe- pitcher for pouring wine.

Loutrophoros- "carrier of washing water"

Lebes Gamikos- marriage bowl, ritual vase for carring water to the bridal bath.

Lekythos- small vase for perfumed oils.

Alabastron- oil vase

Aryballos- small vase with rounded base for pouting and holding oil.