Learn Hardcore Japanese: sono taiken ha husigi da to omoimasu.

は: sets up a topic, a bit more neutral and explanatory.
が: focuses on that specific thing as the one that is strange (often contrastive, like that one in particular).

For a simple sentence like this, は is very natural because we are just commenting on that experience as the topic.

Why is there だ before と思います? Can I say その体験は不思議と思います without だ?

You need だ here because 不思議 is a na-adjective / noun-like word.
The pattern is:

Noun / Na-adjective + だ + と思います

So:

不思議だと思います → I think (it is) mysterious.

You cannot say 不思議と思います in standard Japanese; it sounds ungrammatical.

Compare:

静かだと思います (I think it is quiet.) – 静か is a na-adjective.
学生だと思います (I think (they are) a student.) – 学生 is a noun.

With i-adjectives, you do not add だ:

高いと思います (I think it is expensive.) – 高い is an i-adjective.

My textbook said you often drop だ before と思います. Why do many people say 不思議だと思います instead of 不思議と思います?

Your textbook is talking about nouns and na-adjectives vs. i-adjectives:

For i-adjectives, you do not use だ:
- おいしいと思います (correct)
- おいしいだと思います (wrong)
For nouns / na-adjectives, you do use だ:
- 不思議だと思います (correct)
- 不思議と思います (wrong)
- 学生だと思います (correct)

So the rule is not “you drop だ before と思います”; it is:

Never use だ after i-adjectives.
Use だ after nouns and na-adjectives when they are followed by と思う / と思います.

Why is と used with 思います? What does と mean here?

Here と is the quotative particle. It marks what you think, say, feel, hear, etc. as a “quote” or content.

Pattern:

[Sentence / phrase] + と + 思います
→ I think that [sentence / phrase].

In this sentence:

不思議だ is the content.
と marks that content.
思います is the verb to think.

So 不思議だと思います literally feels like:
I think “it is mysterious.”

The same と is used with verbs like:

言う (to say): そうだと言いました。 – He/She said “That’s so.”
聞く (to hear): 本当だと聞きました。 – I heard (that) it is true.

Where is “I” in this sentence? Why is there no 私?

Japanese often omits the subject when it is clear from context.

その体験は不思議だと思います。

In most situations, the default interpretation is:

I think that experience is strange/mysterious.

You can explicitly say:

私はその体験は不思議だと思います。

but that sounds a bit heavier and sometimes overly explicit, unless you need to contrast with someone else’s opinion:

私はその体験は不思議だと思いますが、彼は普通だと言っています。
I think that experience is strange, but he says it’s normal.

What is the difference between 思う and 思います here?

They are the same verb in different levels of politeness:

思う – plain (dictionary) form, casual.
思います – polite form.

So:

その体験は不思議だと思う。 – casual
その体験は不思議だと思います。 – polite

You choose based on who you are talking to:

Friends / family: 思う is common.
Teachers, coworkers, strangers, formal situations: 思います is safer.

Can I say その体験は不思議だと思う instead? Is it different in meaning?

Yes, you can say:

その体験は不思議だと思う。

The meaning (I think that experience is strange/mysterious) is the same.
The difference is only politeness:

思う → casual / plain.
思います → polite.

Use 思う with close friends or in informal writing (diaries, notes to yourself, etc.).
Use 思います in most public, professional, or respectful situations.

What is the nuance of 不思議? Is it just “strange”?

不思議 has a nuance of mysterious / hard to explain / puzzling, often with a slightly soft or neutral feeling. It can be positive, neutral, or mildly negative depending on context.

Comparison with other words:

不思議: mysterious, hard to understand, almost magical or uncanny.
- その体験は不思議だ – That experience is so mysterious / hard to explain.
変(だ): strange, odd, weird (often more negative or at least more “off”).
- その体験は変だ – That experience is weird / odd.
おかしい: funny, odd, suspicious (context decides).
- その話はおかしい – That story is strange / suspicious or That story is funny.

For a maybe spiritual, unusual, or hard-to-explain experience, 不思議 is very natural.
For something just weird or off, 変だ might be more appropriate.

What part of speech is 不思議? Why is it 不思議だ and not something like 不思議い?

不思議 is a na-adjective (形容動詞). Na-adjectives behave like nouns plus だ / です.

Pattern:

不思議だ – plain form.
不思議です – polite form.
不思議な体験 – a mysterious experience.

So:

不思議だと思います。 – I think (it is) mysterious.
不思議な体験だと思います。 – I think it’s a mysterious experience.

It is not an i-adjective, so it does not become 不思議い.
I-adjectives are words like 高い, 新しい, 暑い, etc., which end in 〜い and conjugate differently.

Could I say 不思議な体験だと思います instead? How is that different?

Yes, you can say:

不思議な体験だと思います。

Difference in nuance:

その体験は不思議だと思います。
→ Topic is その体験. You are saying “As for that experience, I think it is mysterious.”
不思議な体験だと思います。
→ You are describing the experience itself as a mysterious experience. Often used when the experience has just been mentioned and you’re giving your opinion:
I think (it) is a mysterious experience.

Both are natural; the first is more clearly “that experience (we’re talking about) is mysterious,” the second is worded more like “it’s a mysterious kind of experience.”

Can I change the word order, like 不思議だとその体験は思います?

No, that word order is not natural.

In this structure, the pattern is:

[Topic] は [Clause] と思います。

or simply:

[Clause] と思います。

So natural patterns are:

その体験は不思議だと思います。
不思議だと思います。 (if context already makes it clear what “it” is)

But 不思議だとその体験は思います sounds unnatural and ungrammatical.
The と needs to link directly to 思います, and は usually comes earlier, right after the topic.

If I make it a question, should I say その体験は不思議だと思いますか or その体験は不思議だと思いますか？ What does that mean?

The question form is:

その体験は不思議だと思いますか。
(Do you think that experience is mysterious/strange?)

The か at the end makes it a question. The rest of the structure is the same:

[Clause] + と + 思いますか → Do you think that [clause]?

Be careful:

その体験は不思議ですか。
→ Is that experience strange/mysterious? (Asking directly if it is.)
その体験は不思議だと思いますか。
→ Do you think that experience is strange/mysterious? (Asking about the listener’s opinion.)

Could I say just その体験は不思議です instead of using と思います? Is there a nuance difference?

Yes, you can:

その体験は不思議です。
→ That experience is mysterious/strange.
その体験は不思議だと思います。
→ I think that experience is mysterious/strange.

Nuance:

不思議です sounds more like a statement of fact.
不思議だと思います clearly marks it as your opinion. It’s often a bit softer or more polite in tone, because you are presenting it as what you think, not as an absolute fact.

In conversation, 〜と思います is very common when giving opinions, especially in polite speech.