Assume, like presume, has taken on various senses in its history. When we say ‘I assumed he will not be interested’ we are using it in a similar sense as presume (i.e. take it for granted) and when someone assumes an office or new responsibilities he is taking on new responsibilities (of the office).
Similarly, if someone assumes a tough stance or assumes a cooperative attitude they have adopted or taken on a tough/cooperative stance/attitude and when someone assumes an identity they (take someone else’s identity and) pretend to be them. Assumption too is used in similar senses, as in the phrases ‘could you substantiate that assumption’ (supposition), or ‘his assumption (taking on) of office triggered a wave of unrest’.
You may also have heard people being described as unassuming. What does that really mean? Assuming in unassuming carries the sense of ‘pretension (as in the phrase ‘assumed identity’), thus an unassuming person lacks pretension or in other words is down-to-earth and modest.
The word resumption (as in, the Prime Minister has agreed to resumption of dialogues) comes from resume which literally means ‘take (on) again’ (as in, the play resumed after tea or the border talks have resumed after a two year gap etc). And if we replace the prefix re- with sub- we get subsume (take under or include something (smaller) in something bigger) as in “GST — a new uniform indirect tax rate — will subsume excise, service tax, state VAT, entry tax, octroi and other state levies.”
Assume, Assumption*, Unassuming*
Resumption, Resume, Subsume**
*These words are used relatively frequently in Academic English and also appear often in admission tests such as GRE, GMAT, CAT, SAT etc.