あまり・全然 〜ない
not very, not at all
あまり / 全然 + negative
Sign up free to review this point on a spaced schedule.
あまり with a negative softens it to "not very" or "not much": あまり高くない, "not very expensive"; あまり見ません, "I don't watch it much". 全然 makes it total: 全然分からない, "I don't understand at all".
Both need a negative verb or adjective later in the sentence. とても ("very") is their positive partner and can't be used with a negative: とても高くない is wrong.
あまり is also the polite way to say you don't like something: あまり好きじゃないです sounds far gentler than 嫌いです.
In casual speech, 全然 sometimes appears with a positive to mean "totally": 全然大丈夫, "totally fine".
Examples
この店はあまり高くないです。
This shop isn't very expensive.
フランス語は全然分かりません。
I don't understand French at all.
テレビはあまり見ません。
I don't watch much TV.
昨日は全然寝られなかった。
I couldn't sleep at all last night.
魚はあまり好きじゃないです。
I'm not a big fan of fish.