Levels shoudl be used to set proper white and blacd points for the entire image, and that's about it. Curves is much more powerful, allowing you do do all that levels can do, plus correct color casts & colot temperature, adjust contrast, brighten/darken, and much much more. Curves is *the* one tool that you really do want to spend some time getting to know.
Dodge/burn are necessary when you want to darken or lighten smaller areas. For changes to relatively large areas, I prefer a curves adjustment layer. This has two benefits; first, it's reversible, and second, it's strength is adjustable through the opacity slider. You control what parts of the image it acts on by masking it (a layer mask is created by default with the adjustment layer)
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