ある

to be (things)

Says that a thing or event exists or is somewhere, or that you have something: "there is", "have".

Readings

How to form it

Mark the place with に and the thing with が: 机(つくえ)の上(うえ)に本(ほん)があります (there's a book on the desk).
It also means "have": 時間(じかん)がありますか (do you have time?).
Events use ある too, with で for the place: 明日(あした)、学校(がっこう)でテストがあります (there's a test at school tomorrow).
ある is a godan verb, but its negative is ない, not あらない. See the ない form.

机(つくえ)の上(うえ)に本(ほん)があります。

There's a book on the desk.

時間(じかん)がありますか。

Do you have time?

〜てあるhas been done (on purpose)
After the て-form, ある describes a state someone left on purpose: 窓(まど)が開(あ)けてある.