と思うI think (that)…
と思う is "I think": your opinion or your guess, offered as yours. The thought comes first, in the plain form. What someone else thinks takes と思っている.
your opinion
I think this method is the easiest.
your guess
I think the trains will be crowded tomorrow.
someone else's thought
My mother thinks I am still a child.
How to form it
Plain form + と思う
行くと思う, 行かないと思う, 行ったと思う, 高いと思う. A noun or a な-adjective takes だ: 雨だと思う, 静かだと思う.
Polite
Plain form + と思います
Only the end of the sentence is polite.
To ask
どう思いますか
"What do you think?" Japanese asks "how", not "what".
Whose thought?
At the end of a statement, と思う and と思います are your own thought, so 私は is usually left out. Another person named at the front is who you are thinking about, not who is thinking.
I think my younger brother will go to Osaka next month.
Not "my brother thinks".
What someone else thinks takes と思っている.
I think this movie is interesting.
Your thought.
My younger brother thinks this movie is interesting.
His.
Not said: 弟は、
(My younger brother thinks this movie is interesting.)
と思います can't report his thought.
About yourself, と思っています is a view you have held for a while.
I believe that health matters most.
Not ですと思います
Not said: この
(I think this shop is cheap.)
安いと思います.
I think this town is quiet.
静か is a な-adjective, so it takes だ, not です.
"I don't think…"
English says "I don't think he'll come". Japanese usually puts the ない inside the thought: "I think he won't come".
I don't believe he'll come.
Stronger. You are turning down an idea, often one someone has just put to you.
Asking and answering
In a question, the thought asked for is the other person's.
What do you think about the new schedule?
I think the old one was better.
"I think so" is そう思います. "I don't think so" is そうは思いません.
I think so too.
I don't think so.
Softer than "I think"
People put と思います on opinions far more often than English adds "I think". It doesn't have to mean doubt: it keeps an opinion from sounding like a ruling. In meetings and speeches, たいと思います is "I would like to".
Well then, I would like to begin the meeting.
たぶん・きっと: how sure you are
たぶんprobably
I think it will probably rain tomorrow.
"I thought…"
English shifts "is" to "was" after "I thought". Japanese keeps the thought as it was in your head.
I think I put the key on the desk.
You think so now, about something past.
At that time, I thought the key was on the desk.
You thought so then: ある, not あった.
You're still here? I thought you had gone home.
と思っていた is what you had assumed until just now.
Close neighbours
（よ）うと思うN4
With 行こう it is what you mean to do: "I think I'll go". With plain 行く it is a guess.
I think I'll go to Osaka next month.
でしょう・だろうN5
"Probably". In conversation it can sound like a forecast, so people usually give a guess with と思います.
It will probably rain tomorrow.
と言うN4
What someone said: often the natural way to pass on another person's opinion.
She said that the movie had been very interesting.
Check yourself
1Which sentence says what your sister thinks?
Choose an answer to see why.
2Which one fits?
明日は
Choose an answer to see why.
3Someone insists it will rain tomorrow. Which reply pushes back harder?
Choose an answer to see why.
More sentences
I think the meeting will finish by three.
I don't think he knows the news yet.
I don't think the area near the station is very quiet.
What do you think about this movie?
Apparently Yamada still thinks he made the right decision.