The main philosophy in Islam are
1 God the creator of all (no son, no trinity)
Practice of the 5 pillars of Islam, which are fasting, charity, prayer, acknowledgement that there is one God, pilgramage.
Follow the Quran which is considered the last book from God, the Torah and the bible were the previous books, which islamically speaking were changed, and the Quran was promised to be the last revelation and protected.
To believe that Mohammad was the last prophet of Islam.
The first prophet was considered Adam and continued down the line and Mohammad came after Jesus(which is also considered a prophet as well).
The basic teachings of Islam without getting into a long answer is basically:
Remembering Allah's(God) oneness and greatness. by the way Allah is the "arabic" word for God which is used by arab christians as well, and by doing that the 5 times a day prayer plays the most important part of worshipping Allah.
To be good to all mankind including family, friends and others,
To help others.
Just because someone is a muslim doesnt guarantee him a place in paradise, its his good deeds that shall out weigh his bad deeds that will get him a place in paradise.
We must earn our place there by doing the above, if not we will be in hell fire.
Thats it in a nutshell.
Source: I am a muslim!