Seoi-nage (背負投), the shoulder throw.

Nage-waza (throwing techniques), Te-waza (hand techniques), Gokyo 1st set (Dai-ikkyo).
Required for: 8th Mon (orange belt, British Judo Association); 12th Mon (green belt, British Judo Association); 4th Kyu (orange belt, JudoScotland); 3rd Kyu (green belt, JudoScotland); 1st Dan (black belt, British Judo Association); 2nd Dan (black belt, British Judo Association); 3rd Dan (black belt, British Judo Association); 4th Dan (black belt, British Judo Association); 5th Dan (black belt, British Judo Association).

About
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Tori turns in, loads uke onto the back at the shoulder, and throws forward over the shoulder line: one of the most used contest throws in judo.

Step by step (standard right-handed form)
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1. From a right-handed grip, pull with both hands so your partner's weight comes forward onto their toes.
2. Step your right foot across to their right foot, pivot, and swing your left foot back beside it, turning your back into their chest with both knees well bent, your hips below theirs.
3. As you turn, fold your right arm and bring your bent elbow underneath their right armpit, your upper arm snug against their body; the left hand keeps pulling the sleeve forward over your shoulder.
4. Clamp them to your back: their chest against your shoulders, no space between you.
5. Straighten your legs, bow sharply forward and pull both hands down past your left side.
6. They ride over your right shoulder and land on their back in front of you. Keep the sleeve gripped high so their arm is supported through the landing.

Key points
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1. Turn in with bent knees so your hips sit below uke's
2. Keep both elbows in front of your body as you load
3. Finish by straightening the legs and bowing forward

Receiving it
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You are pulled sharply forward onto your toes and their back turns into your chest, their body folding under you; then your feet leave the ground and the world rotates over their shoulder. It is a big forward fall. Stay loose, keep your chin tucked, and let the held right sleeve steer you so you land on your back, left arm slapping wide.

Reference pages elsewhere
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Seoi-nage on the IJF technique reference (International Judo Federation): https://judo.ijf.org/techniques/Seoi-nage

From Waza Book: https://wazabook.com/techniques/seoi-nage/