After

1. Typical mistake: 

I'll phone you after I shall arrive (Or: ...after I shall have arrived). 

After cannot be followed by a future tense. Instead, we use a present tense to express a future meaning. 

I'll phone you after I arrive (Or: ...after I have arrived). 

The same is true of before, until, as soon as, when (in some cases), and if (in some cases). More later...

 2. Typical mistake: 

I'm going to do my exams, and after, I'm going to study medicine. 

After is not usually used as an adverb. Instead, we use afterward, or (and) then, or (and) after that. 

I'm going to do my exams, and then I'm going to study medicine. 

3. Typical mistake: 

After the timetable, the train gets in at half past eight. 

We do not use after to explain what somebody said, or what we have read. Instead, we use according to. 

According to the timetable, the train gets in at half past eight.