Hello Christian,
Thank you for asking such an insightful question!!
I hope my answer will give you a breif look inside that Beliefs of Muslims.
The fist and most important of all beliefs in Islam is the belief in ONE GOD(ALLAH).
We must belive that GOD is self sufficient, He doesnt NEED anything or anyone. He wasnt born nor does he have offspring and he has NO partners.
When we pray to God and seek his help we must pray to God directly, because there are no intermediataries between us and God. Only God has the power to hear and answer our prayers.
GOD see all, hears all and knows all that we do.

Second, The belief in angels
God created the angels to worship him. They do not disobey him, they do not have free will but they only carry out the will of GOD.
The angel Gibreel Is the one who God sent down the message with to the prophets.
There are angels that records everything that we do. These records will be shown to us on the Day of Resurection and we will be held accountable in from of God for them,

Third, The belief In the DIVINE BOOKS

These are books that have been sent by God to his messangers.

1. The Quran, sent to prophet MUHAMMED (PBUH)
2. The Torah, as it was originaly sent to MOSES (PBUH)
3. The Ingeel, The Gosple as it was originaly sent to Jesus (PBUH)
4. Azzaboor, The Pslams as it was originaly sent to Prophet David (PBUH)
5. The Tablet of Abraham (PBUH)

Fourth, The belief in Allahs Messengers

This includes Moses, Jesus, Noah most imporatantly Muhammad

Fifth, The Belief in the last day
This belief necessitates:

a) Believing that this world and all that is in it has an end.
b) Allah, the exalted, will resurrect the creatures once again.
c) The people will be held accountable for their deeds. He who does good, it will be good for him, and he who errs, will suffer the consequences. Everyone will be held responsible for his own deeds.
d) Mankind's deeds are being recorded and will be reviewed by them on the Day of Reckoning.
c) The true believers and Followers of Allah will be in paradise and the enemies or disbelievers of Allah will entre the hell-fire.

The belief in Al Qadar, Divine will and predestination.

This belief is the belief that God has created us and even before we are born he knows what we will do and ow we will choose to live our life. He did creat us with our own free will but God sees and knows all things. He knows if we will choose to follow His will or not.

This issuse canbe kind of complex to explain on a post.

This a a VERY brief discription of the beliefs of Muslims.
Our 'salvation' Truely lies in out belief in Allah and that there is only ONE GOD. And to live as he has instructed us to do so according to his messanger Muhammad.

I hope this helped you in some way. Please feel free to ask more questions!