You can find detailed explanation about that in this article https://www.cryptohopper.com/blog/what-was-the-first-crypto-exchange-449
For sure there's a lot more to learn from past which is amazing to look back.
In late 2013, when I got into bitcoin MTGox was having freezes of withdrawals but it was still operating and people were sending money over there even after it had frozen withdrawals, yet I did not want to get involved in that craziness, but I did get involved with Localbitcoins, which made it easier to connect with individuals for peer to peer trades.
There was also Bitinstant, but it seems that Bitinstant was a bit before my time too.. but I recall the surprise of Charlie Shrem's arrest in January 2014. https://en.wikipedia.org/wiki/Charlie_Shrem