Bodyweight squats, also known as free or air squats, are possibly the most primal and basic exercise you could do. They require good flexibility in the hips, heels and back, and no equipment at all.
You should master free squats before doing any other lower body exercise, as a good squat is the foundation of many exercises. Chances are that if you can't free squat correctly, you won't be able to do many other lower body exercises correctly, and that something is wrong in your body.
To squat with proper technique, set your feet at shoulder width pointing slightly outwards. Start the movement by bending at the hips and pushing them backward as much possible, until you reach a point where you must bend your knees. Do so while keeping your shins as vertical as possible, and never lift your heels. Remember to focus on pushing the floor through your heels. Finally, keep your back as straight as possible, and don't lean too much forward.
When squatting, go at least as low as parallel, this is where the top of your knees is at the same level that the upper crease of your hips. Don't go ass to grass, i.e. as low as you can, when your hammies touch your calves, if doing this causes you pain.
Here is a video where I show you how to progress from zero to a point where you can perform a full squat.
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