The Quran

وَأَنزَلنا إِلَيكَ الكِتابَ بِالحَقِّ مُصَدِّقًا لِما بَينَ يَدَيهِ مِنَ الكِتابِ وَمُهَيمِنًا عَلَيهِ ۖ فَاحكُم بَينَهُم بِما أَنزَلَ اللَّهُ ۖ وَلا تَتَّبِع أَهواءَهُم عَمّا جاءَكَ مِنَ الحَقِّ ۚ لِكُلٍّ جَعَلنا مِنكُم شِرعَةً وَمِنهاجًا ۚ وَلَو شاءَ اللَّهُ لَجَعَلَكُم أُمَّةً واحِدَةً وَلٰكِن لِيَبلُوَكُم في ما آتاكُم ۖ فَاستَبِقُوا الخَيراتِ ۚ إِلَى اللَّهِ مَرجِعُكُم جَميعًا فَيُنَبِّئُكُم بِما كُنتُم فيهِ تَختَلِفونَ

Muhammad Asad

And unto thee [O Prophet] have We vouchsafed this divine writ, setting forth the truth, confirming the truth of whatever there still remains of earlier revelations and determining what is true therein.¹ Judge, then, between the followers of earlier revelation in accordance with what God has bestowed from on high,² and do not follow their errant views, forsaking the truth that has come unto thee. Unto every one of you have We appointed a [different] law and way of life.³ And if God had sowilled, He could surely have made you all one single community: but [He willed it otherwise] in order to test you by means of what He has vouchsafed unto, you.⁴ Vie, then, with one another in doing good works! Unto God you all must return; and then He will make you truly understand all that on which you were wont to differ.⁵

The participle muhaymin is derived from the quadriliteral verb haymana, "he watched [over a thing]" or "controlled [it]", and is used here to describe the Qur'an as the determinant factor in deciding what is genuine and what is false in the earlier scriptures (see Manar VI, 410 ff.).
Lit., "judge, then, between them...", etc. This apparently applies not merely to judicial cases but also to opinions as to what is right or wrong in the ethical sense (see note 55 above). As is evident from the mention of the "followers of the Gospel" in the preceding verse, and of the Torah in the earlier passages, the people spoken of here are both the Jews and the Christians.
The expression "every one of you" denotes the various communities of which mankind is composed. The term shir'ah (or shari ah) signifies, literally, "the way to a watering-place" (from which men and animals derive the element indispensable to their life), and is used in the Qur'an to denote a system of law necessary for a community's social and spiritual welfare. The term minhaj, on the other hand, denotes an "open road", usually in an abstract sense: that is, "a way of life". The terms shir'ah and minhaj are more restricted in their meaning than the term din, which comprises not merely the laws relating to a particular religion but also the basic, unchanging spiritual truths which, according to the Qur'an, have been preached by every one of God's apostles, while the particular body of laws (shir'ah or shari'ah) promulgated through them, and the way of life (minhaj) recommended by them, varied in accordance with the exigencies of the time and of each community's cultural development. This "unity in diversity" is frequently stressed in the Qur'an (e.g., in the first sentence of 2:148, in 21:92-93, or in 23:52 ff.). Because of the universal applicability and textual incorruptibility of its teachings - as well as of the fact that the Prophet Muhammad is "the seal of all prophets", i.e., the last of them (see 33:40) - the Qur'an represents the culminating point of all revelation and offers the final, perfect way to spiritual fulfilment. This uniqueness of the Qur'anic message does not, however, preclude all adherents of earlier faiths from attaining to God's grace: for - as the Qur'an so often points out - those among them who believe uncompromisingly in the One God and the Day of Judgment (i.e., in individual moral responsibility) and live righteously "need have no fear, and neither shall they grieve".
I.e., "in order to test, by means of the various religious laws imposed on you, your willingness to surrender yourselves to God and to obey Him" (Zamakhshari, Razi), "and thus to enable you to grow, spiritually and socially, in accordance with the God-willed law of evolution" (Manar VI, 418 f.).
Lit., "inform you of that wherein you used to differ" (cf. surah 2, note 94). Thus, the Qur'an impresses upon all who believe in God - Muslims and non-Muslims alike - that the differences in their religious practices should make them "vie with one another in doing good works" rather than lose themselves in mutual hostility.