The Smith machine squat will allow you to safely squat a heavy weight in the absence of a spotter. Just make sure that you use the safety pins.
The trap bar farmer's walk is a great whole-body exercise for improving functional fitness, enhancing unilateral leg strength, and boosting overall strength.
The trap bar deadlift is great for building glutes, legs, back and forearms; strengthening the core; improving functional fitness; and developing strength.
Use the dumbbell box squat to eliminate the stretch reflex, making the exercise more difficult and allowing you to overload your muscles with less weight.
Use the barbell step-up to develop balance, coordination, core strength, and unilateral lower body strength.
The lunge is a brilliant exercise, helping you to develop coordination, balance, and the unilateral (one-sided) functional strength of your lower body.
Use the barbell front box squat to strengthen your front squat strength. It's also useful if you have knee problems, as it requires less weight.
The bodyweight squat is great for learning the very basics of squat form, such as how to keep your head up and torso upright as you descend.
Targeting your quadriceps, the jump squat (aka squat jump) is a brilliant compound bodyweight exercise with which you can develop lower-body power.
Easier to set up than the barbell one-leg hip thrust, the weighted one-leg hip thrust is a unilateral isolation exercise that targets your gluteus maximus.
The twisting cable overhead press is brilliant for developing unilateral upper-body strength, as well as for improving core strength and stability.
Use the barbell one-leg hip thrust for unilateral glute and quad activation. Avoid going very heavy because it can place too much torque on your vertebrae.