An AMM or, Automated Market Maker, allows digital assets to be traded in a permissionless and automatic way by using liquidity pools rather than a traditional market of buyers and sellers. AMM users supply liquidity pools with crypto tokens, whose prices are determined by a constant mathematical formula. Liquidity pools can be optimized for different purposes, and are proving to be an important instrument in the DeFi ecosystem.
Vitalik Buterin, the founder of Ethereum, first conceptualized AMMs in a blog post on June 22nd, 2017. The first ever AMM deployed 1 year later, which was Uniswap. Since this breakthrough, the decentralized exchange model has been replicated numerous times on nearly every single blockchain. Vitalik's iteration of the famous x*y=k can be expanded to:
tokenA_balance(p) * tokenB_balance(p) = k
A vital tenant to DeFi is decentralization, so the centralized orderbook method of trading will require an intermediary and will put the decentralization aspect at risk. AMMs offer a decentralized solution to this problem.
The autonomy of AMMs rely on pools of liquidity that are ready to be used. AMMs rely on liquidity providers (LPs) to obtain all of this liquidity. There is no intermediary. Using smart contracts, AMMs pool and balance liquidity to ensure the ratio of assets and price is maintained. AMMs, e.g. Uniswap, use the equation x*y=k to complete this. Liquidity providers have incentives to supply liquidity pools. As a result of this, liquidity pools provide instant access to liquidity. EtherDelta attempted an order book style exchange before AMMs were popularized, but it was difficult to maintain liquidity.