When do you use Eso and Aquello?
I was taught that the words for "that" are ese/esa or aquel/aquella, but I've seen a lot of sentences using eso and aquello. What is the difference and when do you use each one?

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You may use 'ese/esa', 'aquel/aquella' either as demonstrative adjectives or pronouns (that is, you may or may not add a noun after them). 'Ese libro' vs. 'Ése', 'Aquella casa' vs. 'Aquella'.

You can only use 'eso/aquello' as pronouns, so we never add a noun after them. For instance, it would be incorrect to say 'Eso libro'.

By the way, I could certainly point to a distant object and say 'Eso'.

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Ambos son pronombres demostrativos propiamente dichos de una forma neutra.
"eso" denota cercanía de lo señalado. 
"aquello" denota distancia de lo señalado.

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aquello/a= algo que lejos
eso=algo que está cercano