Let's define abnormal behavior, mental problem, mental illness

What is abnormal behavior ? What are mental problems ? What is mental illness ?

These are very subjective term. There is no quantifiable means by which one can say that a persons behavior is appropriate. Perhaps from his perspective he would be right but from others he would be wrong.  

History is full of examples, where, the behaviors seen as appropriate at one time by the societies were totally disowned or abandoned at some other point of time.

1. Killing the slaves and punishing by inflicting pain was appropriate behavior at one point of time,  but not today.
2. Some societies were cannibals ... but today such behavior would put you behind the bars.
3. Duel fights of 16th century Europe. Is it possible today ?
4. Homosexuality was banned in last century but today it has been an acceptable behavior.

So what should we do ? Right and wrong depends on the perspective ... and this is a topic of philosophy …  Perhaps in quest of this answer only ... people would have started studying behaviors  which further would have emerged in a full fledged science called Psychology.

Religions also preaches philosophy of living ... appropriate way of behaving ... and perhaps that's why ... religion ... Philosophy ... and Psychology are linked ...

But still the question persists ... What is abnormal behavior ? What are mental problems ? What is mental illness ?

There are certain words I know know : Depression, anxiety, stress. 
Anorexia, Border line, Schizophrenia, memory loss.

"Mental illness, is a result of Mal-adaptation. There are a bunch of models within psychology for conceptualization of mental illness."