Italian uses two similar words to talk about the soul or the spirit: animo (soul) and anima (soul, spirit). They basically mean the same thing, but if you look at the dictionary entries, each word has further translations that are more specific. 

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They may be interchangeable in certain cases, but there are expressions that always use one or the other, such as stato d'animo. (We'll look at expressions with anima in another lesson.)
 

...e attraversando i pensieri, gli stati d'animo.

...and going over one's thoughts, one's states of mind.

Captions 20-21, Federica Reale - Io e la mia Pupezza

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Stato d'animo does mean "state of mind" but it also means "mood" — where you're at psychologically or emotionally — or "frame of mind." We're talking about the non-physical aspects of how one is feeling.Non ho lo stato d'animo per iniziare un progetto nuovo.

Non sono nello stato d'animo per iniziare un progetto nuovo.
I'm not in the right frame of mind to start a new project.
I'm not in the mood to start on a new project.

Being in the mood is important to be able to communicate, so stato d'animo is a good phrasal noun to have in your vocabulary.

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Anima and animo are so similar that we might not notice the difference. That's why this lesson happened. Now you know!