Hi Saleh,
"Assume" would be to take for granted that something is true even without full evidence. Things that we "assume" may turn out to be false.
Example: Do not assume that every student in a class has the same level of proficiency. / In my hurry, I assumed that my keys were with me.
"Presume" would be to suppose that something is true based on the likelihood or probability that it is true and the absence of proof that it is wrong. Also, we sometimes "presume" something to be true so that we can extend our discussion to other ideas and theories.
Example: Based on the eyewitnesses' accounts, investigators presumed that there were three male perpetrators. Based on this presumption, investigators eliminated all other female suspects.
"Assume" also means to take up a responsibility or role. We cannot use "presume" for this meaning.
Example: He will assume (not presume) the role of CEO with effect from next Monday.
"Presume" also refers to someone's character as being arrogant, having a sense of self-entitlement or demanding unreasonably. We cannot use "assume" for this meaning.
Example: Don't presume (not assume) when you are just a tenant in my house!
I hope this helps.