Thinking is one the skills that human beings can be proud of. While it's debatable whether the lesser creatures can really think, humans have the capacity to think in many different ways. So the way the verb 'think' is used differs a little depending on the kind of thinking involved.
Although 'think' can be followed by either 'about' or 'of', these two prepositions aren't always interchangeable; while they both appear in some cases, often there's a difference in the contexts they're used in.
For example, when 'considering' is what you have in mind, both prepositions are possible.
They should think more about/of their future.
She's thinking about/of retiring.
'Thinking about' (or 'over') is usually the norm where trying to find a solution is the motive.
I've been thinking about/over this problem for a long time.
We'll have to think about it. / We'll have to think it over.
And 'of' is common in senses like 'imagine', 'come up with', 'notice', 'remember', 'focus on' etc.
We couldn't think of (imagine, come up with) a way to solve the problem.
He was the first to think of (notice) these potential problems.
I just couldn't think of (remember) her name.
I wasn't thinking of (focusing on) anyone in particular when I said that.
One's opinion of something may often be expressed with 'think of', but sometimes 'think about' also occurs in this regard.
What do you think of/about that book?
They'll never think of us the same way again.
She thinks highly of his work.
I don't think much of politics.
(Image credit: Robert Couse-Baker)