Greetings Zabel, and a belated welcome to the forum.
Just take that second i off, like this, Alhamdulillah. It means "praise be to Allah".
Al is the definite article meaning "the" (sometimes contextually translated as all).
Hamd is praise.
li is for, or to, and when put together with Allah, is grammatically contracted into lillah.
It's used to give thanks, when we see something good, are happy about something, or simply as a phrase to praise Allah by.
It's also the first words of the first chapter of the Qur'an, the opening chapter, called Surah al-Fatiha:
Alhamdulillahi Rabbil 'aalameen, meaning: "Praise be to Allah, Lord of the Worlds,"
We recite Surah al-Fatiha in every unit of our five daily prayers.