〜たあとで
After doing somethingmachine translation
FormationVerb た-form + あとで / Noun + の + あとで
Verb た-form + あとで means "after…": 食べたあとで (after eating), したあとで (after doing). With nouns, use noun + の + あとで: 仕事のあとで (after work), 授業のあとで (after class). The verb is always in the た-form, even when the whole sentence is about the future.
You already learned 〜てから at N5 — also "after". The nuance differs: 〜てから emphasizes the sequence "finish A, and only then do B", with the two actions usually tightly linked; 〜たあとで simply says B happens after A. In many sentences the two patterns are interchangeable.
で can be omitted, especially in speech: 食べたあと、散歩しました is perfectly natural.
Examples
宿題をしたあとで、テレビを見ます。
After I finish my homework, I watch TV.
昼ご飯を食べたあとで、少し散歩しました。
After eating lunch, I took a short walk.
仕事のあとで、友達とお酒を飲みに行きました。
After work, I went out drinking with friends.