There are two classes of light armor, metallic and non-metallic. Chainmail, Elven, Mithril and Glass are all examples of metallic light armor. You may be surprised to think that Glass can be thought of as metallic, but appearances are deceiving. What we call Glass is nothing like the windows panes you see in houses. The greenish material is far stronger and has a much higher melting point.
Non-metallic armors are Fur and Leather. For these armor types, the hammer is less useful than the sewing kit. A sharp awl is necessary to restitch the thick material. Holes frequently have to be patched with spare material. The rule of thumb is once you have to patch a patch, it's time to throw out the armor and get a new set.
Metallic armor will occasionally need a patch. Usually it can be repaired by hammering the torn pieces back together. Elven and Mithril will repair better when heated. Chainmail is usually malleable enough to work on cold.
The trickiest of all is Glass. Hammer blows struck across the grain run the risk of shattering the armor. Whenever possible, allign the hammer blows with the grain. In extreme cases, place the armor in tub of oil. Place the anvil so that the affected piece is on the anvil, but just under the oil. Vibrations from the hammer blows are absorbed by the oil and less likely to shatter the Glass.