An adverb meaning 'too' or 'excessively' (often used as 'あまりに〜' or 'あまりに〜すぎる'); somewhat formal/written.
あまりに暑くて、外で長くいられない。
It's so hot that I can't stay outside for long.
彼の言葉はあまりに厳しく、傷ついた人も多い。
His words were excessively harsh and many people were hurt.
あまりに驚いて声も出なかった。
I was so surprised that I couldn't make a sound.