Swimming

Swimming is needed to enter and cross deep water without a Boat or Raft.

In-Game Text
"Having learned how to catch the fish, he next strove to be like one."

Swimming allows your character to cross deep water. Swimming is highly draining on your stamina, so know your limits, and don't brave waters you cannot handle.

Health Warning
Drowning (running out of stamina while in deep water) will kill your character over time, additionally leaving no corpse to retrieve items from.  It is highly advisable to not even buy swimming  until much later. High constitution is advised (upwards of 100) merely for crossing rivers. The best way to test swimming capabilities is by equipping a Silver for the Ferryman, saving your character in case of drowning.

You cannot quick-travel while swimming, meaning the only safe exit would be by resurfacing (by shallow water, or boat). You also cannot drink to restore stamina while swimming.

loftar has stated: "The "formula" for swimming is 3%/CONS per integral coordinate (whereas one tile is 11x11 in that system) while moving, plus 10%/CONS for each 600 ms while you're in the water."