When you vacuum the pool the algae returns the next day how come?

Vacuuming just moves the visible algae to the filter. It does not kill it. You need to shock the pool and treat with algaecide. Brush pool thoroughly and vacuum up dead algae. Then clean your filters. It may take more than one treatment to kill all the algae. Also have your pool tested for phosphates. Phosphates are basically food for algae. If algae has a good food source, it can survive in even high amounts of chlorine.

Therefore, you may also need to treat for phosphates.

It would be best to take a water sample to a retail pool store such as Leslie's. They will give you printout of what your pool needs, amounts or chemicals, and order to apply them.