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Intro
Table of Contents
About the Authors
About This Book
Chapter 1: Introduction to AMMs
1.1 Preliminary Notions
1.2 Historical Overview
1.3 Summary
Chapter 2: Uniswap v2
2.1 Trading in a Uniswap v2 pool
2.1.1 Spot Price
2.1.2 Accounting for Fees
2.2 Impact of the Trades on the Price
2.2.1 A Simple Example
2.2.2 Analysis of Two Consecutive Trades
2.2.3 Impact of the Trade Size on the Average Purchase Price
2.2.4 Impact of the Trade Size on the Average Sell Price
2.2.5 Impact of the Trade Size on the Price Growth Ratio

2.3 Providing Liquidity
2.3.1 Minting LP Tokens
Starting the Pool
2.3.2 Burning LP Tokens
Distribution of Fees
2.3.3 Pool Value and Impermanent Loss
Computing Impermanent Loss Without Fees
Accounting for Fees
2.3.4 LP Token Swap
Common Token Case
No In-Common Token Case: Oracle Swap
2.4 Motivating DEX Aggregators
2.5 Summary
Chapter 3: Balancer
3.1 The Constant Value Function
3.2 Spot Price
3.2.1 Constant Value Distribution
3.3 Trading Formulae
3.4 Providing Liquidity
3.4.1 All-Asset Deposit
3.4.2 Single-Asset Deposit

3.4.3 All-Asset Withdrawal
3.4.4 Single-Asset Withdrawal
3.5 Pool Tokens Swap
3.5.1 Swap of Pool Tokens That Belong to Pools of Different Types
3.6 Summary
Chapter 4: Curve Finance
4.1 The StableSwap Invariant
4.2 Mathematical Preliminaries
4.2.1 Finding the Parameter D
4.3 Trading Formulae
4.3.1 Taking Fee into Consideration
4.4 All-Asset Deposit
4.5 All-Asset Withdrawal
4.6 Single-Asset Withdrawal
4.7 StableSwap LP Token Swap
4.8 Summary
Chapter 5: Uniswap v3
5.1 Ticks
5.1.1 Initialized Ticks
5.1.2 Tick Spacing

5.2 Liquidity Providers' Position
5.3 Impermanent Loss
5.4 Multiple Positions
5.5 Protocol Implementation
5.5.1 Variables
5.5.2 Fees
5.5.3 Trades
5.5.4 The swap Function
5.5.5 Example
5.6 LP Tokens
5.6.1 Minting LP Tokens
5.6.2 Modifying the Position: Part I
5.6.3 Update the Position
5.6.4 Tick Class
5.6.5 Burning LP Tokens
5.7 Analysis of Liquidity Provisioning
5.7.1 Capital Efficiency
5.7.2 Independence with Respect to Other Liquidity Providers
5.8 Summary
References
Index

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