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Automated Market Makers (AMMs) are the underlying protocols used by Decentralized Exchanges (DEX) to allow users to perform trades of cryptocurrencies in a decentralized way with no middlemen. In a traditional trading market a buy order has to be matched with a sell order to achieve a trade. In other words, a coincidence of wants and needs has to occur, which is not always guaranteed. However, for an Automated Market Maker, users trade against the protocol itself, a smart contract -or rather a community pool of funds- which is, in simple terms, an open source computer program in which mathematical formulas define prices. The critical point is that no banks or intermediaries are necessary, giving crucial financial access to a much larger crowd, regardless of who they are with less barriers to access.In this book, we perform a thorough study and a clear-cut exposition of the principal Automated Market Makers (Uniswap v2 and v3, Balancer, and Curve), giving a detailed description of how they work, unveiling the mathematics behind them and showing plenty of examples as well as novel proofs for several interesting facts. In each chapter, we describe each Automated Market Maker's core idea and derive the mathematical formulas used in the code, giving careful explanations of the logical thinking involved and detailing the steps needed to reach those formulas. All these explanations are complemented with thoughtfully chosen examples which further help to enlighten the readers on how the formulae work. In addition, the relevant parts of the codes of the Automated Market Makers are shown after explaining each formula so that the actual implementation of the formulae can be seen.WHAT YOU'LL LEARN:Learn what AMMs are and how work they How Decentralist Exchanges (DEX) work The principals of Decentralized Finance (DeFi)Grasp mathematical formulae that underpin decentralized exchangesabout Solidity programming languageCurrent industry best practices WHO IS IT FOR: Interested parties, new to Blockchain and Cryptocurrency trading, who want to learn more about AMMsDevelopers who want to dive deeper into the core features of AMM platformsInvestors and venture capitalists who want to know more about new emerging technologies