Travertine is a type of limestone that forms when calcium carbonate separates from water during evaporation. It's formed in areas where there's a combination of limestone and hot springs. The Mammoth Hot Springs of Yellowstone park in the United States is one example. Home builders like travertine because it's durable, elegant and easy to cut. Travertine tile is known for its tiny pock marks and rivets, which gives it great character visually, but poses some cleaning challenges.
Instructions as follows:
                                                   
Firstly, consider sealing your travertine floors with a clear epoxy resin. This will preserve the surface appearance and relieve you of the heavier cleaning required of unsealed travertine.
Secondly, vacuum or sweep your travertine floors frequently. Tiny pieces of sand and dirt can grind their way into the floors and eventually create dirty paths lacking texture and beauty.
Thirdly, create a cleaning solution consisting of warm water and "stone soap'" such as Granite Gold. See Resources for more information.
Fourthly, use a microfiber mop to clean floor grime away (microfiber mops leave less dirt behind than sponge mops). Before you begin, make sure the mop is extremely clean to avoid leaving dirt behind; this will only grind back into the til