I crossed the river at the shallows on foot.
There are many small fish in the shallows.
There is a shallow spot downstream on this river.
The boat ran aground on a shoal and couldn't move.
The children crossed the ford to reach the other bank.
The little child decided to swim in the shallows.
浅瀬 is the common everyday word for a shallow spot in water, while 高瀬 is a rarer, more literary or place-name-like term for the same idea.
浅瀬 refers generally to any shallow part of water, while 遠浅 specifically describes a beach or seabed that stays shallow far out from the shore.
深み is a deep spot in the water, the direct opposite of 浅瀬, a shallow spot.
Compound of 浅 (asa, 'shallow') and 瀬 (se, 'shallows, rapids'). The reading あさせ is a straightforward combination of the kun'yomi readings.