Automated Market Makers (AMMs) are a novel type of market makers that eliminate the need for a coun-terparty in a trade. This thesis analyses the properties of several types of AMMs, and in particular the con-centrated liquidity market maker. An axiomatic definition of AMMs is provided, and two types of constant function market makers (CFMMs), called the constant sum market maker (CSMM) and constant product market maker (CPMM), are explored. The concentrated liquidity market maker, which improves liquidity provision compared to the CPMM, is thoroughly analyzed, and it is shown that it’s trading function can be formulated as a composition of functions. This thesis also conjectures that the concentrated liquidity trading function can be approximated by taking an infinite number of compositions. Additionally, a simulation study is conducted using transaction mocking. The simulation study supports the conjecture, and brings several other noteworthy properties of the concentrated liquidity market maker to light.