1.Prepositional phraseanyway, in any case; indicates a statement is true regardless of other considerations; used to reinforce or explain a point.
"After all, they never come home for Christmas.; Of course he won't give you credit. After all, his first and last concern is his company's profit margin."
2.Prepositional phrasein the end, however; used in referring to something that was believed to be the case, but is not; or to an outcome that is not what was expected or predicted.
"They won't be coming home for Christmas after all."
3.Prepositional phraseIntroduces information that supports the preceding statement.
"Of course he's coming to the party. After all, he did promise."