This is the 2178th most frequent Japanese word.
欲しく
"欲しく" means "wanting" or "desiring."
Here, '欲しくて' conveys a strong desire for the book, combined with an action ('探しました') motivated by this want.
この本が欲しくて、毎日図書館で何度も探しました。
I wanted this book, and I looked for it every day in the library.
In this example, '欲しくない' denies the desire ('to not want'), influencing the decision made regarding purchasing the gift.
彼が欲しくないと言ったので、プレゼントを買うのをやめました。
He said he didn't want it, so I refrained from buying the gift.
The phrase '欲しくと思う' expresses the act of considering or articulating desire.