Who are Liquidity Providers?

Liquidity providers can be anyone who is able to supply equal values of ETH and an ERC-20 token to a Uniswap exchange contract. In return they are given tokens from the exchange contract which can be used to withdraw their proportion of the liquidity pool at any time

What is price slipperage？An example?

Trades on Uniswap cause price slippage, with trades that are large relative to total liquidity causing more slippage. So, for Uniswap to function well and allow large trades it also needs large liquidity pools.

from this example, we find that invariant will change when the transations going on.

eth_liquidity_pool = sqrt(constant_product / eth_price)
token_liquidity_pool = sqrt(constant_product * eth_price)

inpermanent loss

This chart shows that for most of the time since providing liquidity, this account has been in a net negative position (yellow line), compared to just holding the original funds. This is due to the large divergence losses (blue line) created by the ETH price movements (green line) over the period. However, throughout there has been a steady accumulation of fees (red line). With the ETH price recently moving closer to the price at which liquidity was provided, most of the losses have now been reversed.