Open-Transactions is a free software library of financial cryptography primitives, used for implementing cryptographically secure financial transactions.
Open-Transactions also includes a server and client API.
Open-Transactions can be used for issuing currencies/stock, paying dividends, creating asset accounts, sending/receiving digital cash, writing/depositing cheques, cashier's cheques, creating basket currencies, trading on markets, scripting custom agreements, recurring payments, escrow, etc.
Open-Transactions uses strong crypto. The balances are unchangeable (even by a malicious server.) The receipts are destructible and redundant. The transactions are unforgeable. The cash is untraceable. The cheques are non-repudiable. Etc.
Open-Transactions is able to prove all balances, as well as which instruments are still valid, and which transactions are closed, without storing any transaction history (other than the last signed receipt.)
OT can be used to build wallets, market exchanges, and many other things. Basically anywhere you want to build secure transactions, you can use OT.
how does money get into the open transactions network?
Any user choosing to act as an issuer can issue his currency onto OT servers by uploading a signed currency contract and then issuing a number of units. Then any other user can use the same currency contract to open asset accounts denominated in that same currency. (In practice, most users will not issue their own currencies, but simply use existing ones.)
Upcoming additions will enable currency units based on blockchain-based currencies to be issued on OT without an issuer, since the backing reserves will be stored in a multisig voting pool on the blockchain itself. For details on how this will work, see: https://bitcoin.stackexchange.com/a/834/6473
You may also be interested in this: How can Open Transactions benefit Bitcoin?