What sort of naval technology and strategies were present in the European powers during medieval period? What notable battles took place? What were the most important advances? How did ships usually engage one another?
When studying Naval warfare, the biggest name to claim during this time period was the Byzantine Navy.
The ships used by them were the Dromon, considered a large ship between 30-50 meters in length and carried 200 rowers and 50 marines (seaborne infantry, not be confused with Marines i.g. members of the United States Marine Corps).
Now these large ships basically would ram into each other until one ship was immobile or was close enough to get enough marines into the other ship and force them to surrender. In fact it was basically the same Naval tactics used during the great Roman and Greek days of old.
When it came to technology obviously the bigger ship, the bigger ram, which secondarily lead to having more space to carry more marines to board other ships with was the ideal way of building your navy. Although, the most interesting piece of technology would be my little friend called "Greek Fire". Basically medieval napalm that would even burn on top of water. The Byzantine's used this to their advantage.