This is the 6575th most frequent Spanish word.
carlos
"Carlos" is a proper noun, a Spanish given name equivalent to "Charles" in English.
Here, 'Carlos' is again used as a proper noun to indicate the person with whom the subject intends to converse.
Voy a hablar con Carlos mañana.
I am going to talk to Carlos tomorrow.
Here, 'Carlos' is used as a proper noun referring to a specific person named Carlos, the subject of the sentence, who is performing the action of studying.
Carlos está estudiando matemáticas.
Carlos is studying mathematics.
In this instance, 'Carlos' indicates possession, as 'de Carlos' means 'Carlos's,' showing ownership of the book.