This book provides a concise yet thorough introduction to payments and financial market infrastructures, exploring various types of risks, retail payments, payment systems, cross-border payments, central counterparties, FX operations, and central securities depositories. The final chapter investigates payment innovations, including unbacked crypto-assets (e.g. Bitcoin), stablecoins, and central bank digital currencies. The text outlines key activities and risk management frameworks, as well as examining the operational mechanics of different payment systems. The book emphasizes the importance of understanding the nature of transfer of financial claims and liabilities through the process of payment and settlement, providing financial account representations of payments wherever useful. The book concludes that the payment and financial market infrastructure space has been shaken by recent innovations, which are expected to lead to seismic shifts in payment technology, practices, and market structures.