Libraries are similar to contracts, but their purpose is that they are deployed only once at a specific address and their code is reused by various contracts. This means that if library functions are called, their code is executed in the context of the calling contract; that is, this points to the calling contract, and especially, the storage from the calling contract can be accessed. As a library is an isolated piece of source code, it can only access state variables of the calling contract if they are explicitly supplied (it would have no way to name them otherwise).
Libraries cannot have state variables; they don't support inheritance and they cannot receive Ether. Libraries can contain structs and enums.
Once a Solidity library is deployed to the blockchain, it can be used by anyone, assuming you know its address and have the source code (with only prototypes or complete implementation). The source code is required by the Solidity compiler so that it can make sure that the methods...