The moon god worship has been practiced in Arabia about 2000 years ago. At Mecca was the moon god named Hubal, who was Lord of the Kaba. The symbol of the moon god was crescent. Hubal, the moon god was also called Al-Ilah. Allah's name derives from the pagan moon god. The moon god crescent symbol is one of the most important symbols of Islam.

Quran Su 41: 37. among his signs are the night and the day, and the sun and the moon. adore not the sun and the moon, but adore Allah, who created them, if it is him ye wish to serve.

The Quran is a contradiction book, because the Quran teaching also that do not worship the moon, but the Quran urges to swear by the name of the moon.

In the Quran is remains of the evidence, which prove that the Arabs, and Muhammad were also dealing with the worship of the moon:

Quran Su 74:
31 and we have set none but angels as guardians of the fire; and we have fixed their number only as a trial for unbelievers,-- in order that the people of the book may arrive at certainty, and the believers may increase in faith,-- and that no doubts may be left for the people of the book and the believers, and that those in whose hearts is a disease and the unbelievers may say, "what symbol doth Allah intend by this?" thus doth Allah leave to stray whom he pleaseth, and guide whom he pleaseth: and none can know the forces of thy lord, except he. and this is no other than a warning to mankind.
32 nay, verily: by the moon,
33 and by the night as it retreateth,
34 and by the dawn as it shineth forth, -

In the Quran is swearing (an oath) by the name of the moon, as well as the name of the sun. The Bible doesn't prompt you to swear by the name of celestial creatures, but to believe in the Almighty God.

Quran Su 84:
7 then he who is given his record in his right hand,
8 soon will his account be taken by an easy reckoning,
9 and he will turn to his people, rejoicing!
10 but he who is given his record behind his back,--
11 soon will he cry for perdition,
12 and he will enter a blazing fire.
13 truly, did he go about among his people, rejoicing!
14 truly, did he think that he would not have to return to us!
15 nay, nay! for his lord was ever watchful of him!
16 so I do call to witness the ruddy glow of Sunset;
17 the night and its Homing;
18 and the moon in her Fullness:
19 ye shall surely travel from stage to stage.

In Arabia, people worshiped the moon god, and Muhammad wrote verses to Quran that commend the moon. Muhammad's purpose was persuading the Arab tribes to believe his new religion (Islam). That's why he wrote to Quran verses praising the moon. Muhammad also named his religion god for Allah, which derives from the moon god cult. Muhammad did this to please the Arab tribes. The Quran itself bears witness to the fact that some of the basis of Islam comes from the Arab moon god worship. Also the name of Allah derives from the moon god.

You can read the whole article in here: Differences Quran and Bible