Very interesting question. 之 and 以 both have a lot of meanings, here they mean the point or the boundary of time, place or scale. Beside 之后，以后, there are also 之前，以前；之内，以内；之外，以外 etc.. Acturally, 之后 and 以后 mean the same and can be replaced by each other. For example: 1. after they ate dinner they watched telly 吃过晚饭之后，他们看电视 吃过晚饭以后，他们看电视 these two sentences are the same. 2. after that do you still think it's a good idea： 从那以后，你还觉得这是个好主意么？ 从那之后，你还觉得这是个好主意么？ they are the same as well. 3. after her mother passed away, linda become very withdrawn 她妈妈去世以后，Linda变得很内向 她妈妈去世之后，Linda变得很内向 still the same! 后 means the same with them, but it is simlified. Advantage: simple. Disadvantage: lost part of the functions. Let's test the effect of the simlification: 1. 吃过晚饭后，他们看电视 OK 2. 从那后，你还觉得这是个好主意么？ NOT OK 3. 她妈妈去世后，Linda变得很内向 OK Results are: 1. Some of them can be replaced, but not all. 2. Before and After are all normal usages, but sometimes 之后 and 以后 sound a little bit more literary, just sometimes, just a little bit. In order to avoid any mistakes, you can always use 之后 and 以后. To make it simple and sound more natural you can replace it, but not always. I myself have not concluded thoroughly when it can not be replaced by now, may be next time.

translate the scentences: after they ate dinner they watched telly 吃完饭后，他们看望了telly。 after that do you still think it's a good idea：那件事之后，你还觉得这是个好主意吗？ after her mother passed away, linda become very withdrawn在她妈妈去世以后（之后），Linda变得非常的沉默寡言。

actually,when talk about time these words all mean “after”. the differecnce is "以后" usually talk about the future or after a certain event.“之后” also means after a certain time. but, if "之后" is put on the beginning of a scentence, it means after the very thing the previous scentence expresses. besides "之后" can also be used to descripe the space relation. for example "在我之后" means "behind me" "后" is usually used after the word that express a period of time ,for example "两天后" means two days later". Certainly, "后” should not be used at the beginning at any scentence.

i will see you agein sometime 我们以后还会再见面。 i ate beaf potato and then pudding（later） 我先吃了牛肉，土豆，之后又吃了布丁。 后has lots of meaning ， but dont use solo ，with 以后， 然后，之后，后来，etc.and this words are adverb for time ， and 前后左右，后面，for the space。