What is the difference between 阅读, 读, and 看?
看 could mean see, look, watch and read, but 阅读 does not mean see, look or watch. 阅读 only means read. Examples: 


我在看书。(I'm reading a book.)
我在读书。(I'm reading a book.)
我在阅读。(I'm doing some reading.)(Normally we don't say 我在阅读书; see below.)
WRONG SENTENCE: 请阅读那个垃圾桶。(Please read that trash bin.)
请看那个垃圾桶。(Please look at that trash bin.)

阅读 is more like an intransitive verb, or a noun in English, while 读 is more like a transitive verb. Examples:


我喜欢阅读。(I like reading.)
UNNATURAL: 我喜欢阅读书。(I like reading books.)(Although in English it is very good, it sounds weird in Chinese, because a one-syllable word is combined with a two-syllable word.)
RATHER FORMAL: 我喜欢阅读书籍。(I like reading books.)(This sounds formal rather than weird because two two-syllable words are put together.)