Whilst quite an attractive plant, a member of the carrot family (or umbellifereae), ground-elder (Aegopodium podagraria) has something of a reputation! My field guide describes it as "a perennial and pestilential weed of shady places, waysides and all too often, gardens." For the sake of clarity pestilential means "very widespread and troublesome" so ground-elder is undoubtedly a widespread and troublesome weed of cultivation.
This plant has flowers and leaves that resemble those of elder hence its accepted common name but it not related to elder in any way. It is also known by a number of other country name such as herb gerard, bishop's weed, goutweed, and snow-in-the-mountain. The leaves are edible and this was once grown as a crop! It is thought to relieve the symptoms of gout and arthritis if applied as a compress and this accounts for the common name of goutweed.
Ground-elder spreads rigorously by underground rhizomes which are almost impossible to clear. Any small piece left behind will soon re-emerge as a new plant! Other forms of control, poisons, mulches and blanketing are rarely effective. The best way to not have a ground-elder problem is not to let it get in to your garden in the first place.