Hi Trisha,
there is a difference between "wollen" and mögen". To fully explain this, we need the help of a third verb: möchten.
Wollen:
Wollen is close to "want" in English, but the usage is a bit complicated in that it sounds a bit rough to say "I want [something]" because it sounds a bit condescending, like something a parent or boss would say.
"Ich will ein deutsches Buch lesen." sounds weird because it sounds like something was keeping you away from doing it or as if you were ordering someone to get you a German book.
However, it is totally common to use it when talking about other people or a another person and you.
-- "Wollen wir etwas essen gehen?" (Should we eat something?)
-- "Wollt ihr essen gehen?" (Do you want to go eat?)
"Möchten"
This is the polite and most common way to express something you would like to do.
-- "Ich möchte (gern) ein deutsches Buch lesen." is a neutral wish and perfectly fine as that.
Please note that, if you want to say "I would like to read a German book." then "Ich würde gerne ein deutsches Buch lesen." is even slightly better.
Mögen
This is "to like" (something or someone).
-- Ich mag deutsche Bücher.
It is still common in some parts of Germany to say something like:
-- Ich mag ein deutsches Buch lesen.
But that is more of an answer to the question "what would you like to do (now)?" and it sounds a bit childish.
As Marcus correctly stated, "möchte" is actually a conjugation of "mögen" which is probably why it was in your dictionary.
However, since the usage is different from "mögen", I would suggest to treat it like two different verbs.