The hammer is the basic tool. It can be made from stone, logs, lumber or metal. It can be made at the Carpenter or the Machine Shop.
It is actually representative of a basic tool. For instance, you need a hammer to make lumber out of logs.
Hammers are easy to handcraft by foraging for a piece of stone. If you have one in your inventory, like all tools, it applies to processes where applicable. One of the first tools you should make is a hammer. Also, you should make a carpenter that makes hammers out of local resources. When you have a hammer, mining takes much less time as well as other processes, some of which require a hammer.