In our modern day, the two largest religions are Christianity and Islam. These religions connect with a number of similar aspects; however, they also are separated by clear distinctions. Both are derived from Judaism and continue to retain values of Judaism, one value in particular, the monotheistic belief of the one and only powerful being, God. On the Christian side there is of course the Trinity, but I'm not going to get too fastidious. As well as sharing the belief of God (in Islamic beliefs He is called Allah), partisans of Islam and Christianity hold to the belief that God created the world and cares about the lives of all humans.
Although there are disagreements of beliefs between Muslims and Christians, Muslims do believe that Jesus existed without sin, and that He ascended bodily to heaven. However, Muslims believe Jesus was just another prophet of God, and that Muhammad was the final prophet who set the record straight, in the sense of what God has commanded us to believe. From the time of the Prophet Muhammad (around 1,300 years ago) the association of Islam and Christianity has been anything but agreeable.
There are five central tenets of Islam, known as the Five Pillars (different sects of Islam may have added to these five tenets, depending on the sect). The center of all the tenets is the first tenet, which reads: There is no god but Allah and Muhammad is the Prophet of God. Allah refers to God in Arabic. The remaining tenets (translated) are as follows: daily prayer in the direction of Mecca, alms-giving, fasting during the month of Ramadan, and finally, the pilgrimage to Mecca.
Comparison grids of Islam and Christianity can be found here and here; I will list the beliefs and doctrines of these comparisons which I see as most important relative to this blog. Muslims and Christians
B. Kataregga, D. Shenk. Islam and Christianity. Uzima Publishing House, 1980.
Spencer, Harold. Islam and the Gospel of God: A Comparison of the Central Doctrines of Christianity and Islam. I.S.P.C.K., 1976.