For lower body you might want to do some sprints, stairs, hindu squats, and single leg squats (pistols).
For upper body, all that were mentioned were good, but you don't have to leave it at "no equipment"...you have four weeks which I presume to be at home. Make something. Find something heavy and pull it, push it, flip it, whatever.
You might also want to research "gymnastic rings" or "power rings". If you can find somewhere to hang them (trees, jungle gyms, stairs, balconies, etc), then you have the option of having some of the greatest bodyweight training tools ever.