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We characterize digital cash as the digital equivalent of physical cash: secure, fungible, decentralized, directly controlled, privacy-preserving; but enhanced with qualitatively new functionality. It is extremely efficiently transferable and, most importantly, transactional or, more generally, contract-backed. This facilitates fully automated, guaranteed transactional execution of atomic resource exchanges and more complex contracts, without a multitude of intermediaries and expensive or slow semi-manual processes. A didactic objective is separating money characteristics from technology aspects such as specific blockchain and distributed ledger systems to help disentangle discussions of digital money design from implementation techniques. We finally discuss the power and role of programmable (contract-backed) digital money in case studies: tokenization of invoice debt using smart contracts on Ethereum, with stablecoins serving as digital money; smart contracts for disbursing payments transparently and reliably in accordance with social legislation; and a Danish e-krone for crowdfunding public and private community projets. These contributions are made in independent chapters by participants of the Working Group on Digital Cash at Copenhagen FinTech in 2018 and 2019, which have not been published before. Collectively, the contributions illustrate the design space and potential of digital money when powered by smart digital contracts that effectively eliminate both counterparty risk (somebody does not pay or does not deliver) and settlement risk (a trade fails and needs to be aborted) orders of magnitude faster than in current financial practice.