What is Islam's core belief?

The core belief of Islam is submission to God

Islam means submission and calls all muslims those people who submit to God.

Islam means spending the life in accordance with Quran and Sunnah

Islam's core belief is submission to God's law.
By submitting to God's law people will be at peace with their creator, respect themselves and be at peace with themselves, respect others and be at peace with other people and creatures, and respect their environment. Any Diviation from God's law can only harm humanity and the environment.
God sent thousands of messengers to humanity to teach them about His law. The last message is the Quran and the last messenger is Prophet Muhammad (pbuh&HP)
God is the engineer who created the worlds, the sky and what is in between, all living creatures. It is God who gives life and takes it and He will be the Master of the Day of Judgement
For more information on core belief, read a translation of Quran and a translation of Nahjul Balagha, available on internet.