double negatives in japanese

In english, when a sentence has more than one negative, it is bad grammar or the sentence because positive, For example "I don't have no money" that would mean I have money to some people in really bad grammar, is this the same way in japanese? becaause I saw this sentence "あまり好きじゃないです。". Meaning "(I) don't like it very much." Doesn't this sentence have two negatives? "あまり" and "好きじゃない". would the sentence change if "好きじゃない" was just "好き"?

The sentence あまり好きじゃないです has just one negative, じゃないです.

好きじゃないです。I don't like it.
あまり好きじゃないです。I don't like it very much.

あまり is an adverb that is used together with a negative, but by itself it is not a negative :)

げんきじゃないです。I am not well.
あまり　げんきじゃないです。I am not very well.

よくないです。It is not good.
あまり　よくないです。It is not very good.

BTW, double negatives in that case,
好きじゃなくはない
好きじゃないわけじゃない
I don't dislike it or I like it (to some extent)

I do not fully understand grammar of English.
あまり（amari）
One meaning of the word (based on dictionary)
(Accompanied by a word of cancellation after) how especially not enough to say bother.
This is the same meaning as それほど、あんまり.

I'm not native, but as ajapaneseboy pointed out, there do seem to be a lot of double negatives becoming positives in Japanese.

行かないでもない (It's not that I won't go→I may go)
or even
行かなくてはいけない (I can't not go→I have to go)

I don't know that it is a rule though. I feel that there are probably counter examples.

Double-negatives are not exactly unheard of in English either. ;)

ok I see, I thought "amari" was negative and as for the rule, I am alittle unsure how it works but for the most part I get it.

It's all about avoiding direct, confronting situations. Amari makes it 'not really' and must be used with a negative sentence. It's more polite to say you don't really like something instead of saying you dislike something outright (kirai). Similarly, invitations are given in the negative. Ikimasenka = an invitation to go.