Concise Bible Dictionary:

The subject of “law” is not restricted in scripture to the law given by Moses. God gave a commandment (or law) to Adam, which made Adam’s subsequent sin to be transgression. Where there is no law there is no transgression (Rom. 4:1515Because the law worketh wrath: for where no law is, there is no transgression. (Romans 4:15)), though there may be sin, as there was from Adam to Moses: “until the law sin was in the world, but sin is not imputed [or put to account] when there is no law” (Rom. 5:1313(For until the law sin was in the world: but sin is not imputed when there is no law. (Romans 5:13)). This doubtless signifies that specific acts were not put to account as a question of God’s governmental dealings, when there was no law forbidding them. Men sinned, and death reigned, though they “had not sinned after the similitude of Adam’s transgression” (Rom. 5:1414Nevertheless death reigned from Adam to Moses, even over them that had not sinned after the similitude of Adam's transgression, who is the figure of him that was to come. (Romans 5:14)), for no definite law had been given to them. The nations that had not the law were however a law unto themselves, having some sense of good and evil, and their conscience bore witness accordingly. It is not a true definition of sin, to say that it is “the transgression of the law,” as in the AV of 1 John 3:44Whosoever committeth sin transgresseth also the law: for sin is the transgression of the law. (1 John 3:4). The passage should read “Sin is lawlessness:” that is, man doing his own will, defiant of restraint, and regardless of his Creator and of his neighbor.
“Law” may be considered as a principle in contrast to “grace,” in which sense it occurs in the New Testament, the word “law” being often without the article (though the law of Moses may at times be alluded to in the same way). In this sense it raises the question of what man is for God, and hence involves works. “The doers of [the] law shall be justified” (Rom. 2:1313(For not the hearers of the law are just before God, but the doers of the law shall be justified. (Romans 2:13)); but if, on the other hand, salvation be “by grace, then is it no more of works: otherwise grace is no more grace” (Rom. 11:66And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then is it no more grace: otherwise work is no more work. (Romans 11:6)). The conclusion is that “by the deeds of [the] law there shall no flesh be justified in his sight.” None can be saved on that principle. In opposition to it “the righteousness of God without [the] law is manifested.” The believer is “justified freely by his grace through the redemption that is in Christ Jesus” (Rom. 3:20-2420Therefore by the deeds of the law there shall no flesh be justified in his sight: for by the law is the knowledge of sin. 21But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets; 22Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference: 23For all have sinned, and come short of the glory of God; 24Being justified freely by his grace through the redemption that is in Christ Jesus: (Romans 3:20‑24)). “Law” as a principle stands also in scripture in contrast to “faith.” “The just shall live by faith: and the law is not of faith; but the man that doeth them shall live in them” (Gal. 3:1111But that no man is justified by the law in the sight of God, it is evident: for, The just shall live by faith. (Galatians 3:11)).
The word “law” is also used for a fixed and unvarying principle, such as “a law of nature”; thus we read of the “law of faith,” “law of sin,” “law of righteousness,” “law of the Spirit of life,” (compare Rom. 7:2121I find then a law, that, when I would do good, evil is present with me. (Romans 7:21)).
The term “law” is occasionally used in the New Testament as a designation of other parts of the Old Testament besides the Pentateuch. The Lord said, “Is it not written in your law, I said, Ye are gods?” when the quotation was from the Psalm. John 10:3434Jesus answered them, Is it not written in your law, I said, Ye are gods? (John 10:34): similarly 1 Corinthians 14:2121In the law it is written, With men of other tongues and other lips will I speak unto this people; and yet for all that will they not hear me, saith the Lord. (1 Corinthians 14:21).
The LAW OF LIBERTY, (James 1:2525But whoso looketh into the perfect law of liberty, and continueth therein, he being not a forgetful hearer, but a doer of the work, this man shall be blessed in his deed. (James 1:25); James 2:1212So speak ye, and so do, as they that shall be judged by the law of liberty. (James 2:12)), implies that, the nature being congruous, the things enjoined, instead of being a burden, are a pleasure. Doing the commandments of the Lord is the fruit of the divine nature: they are therefore both law and liberty.

Strong’s Dictionary of Greek Words:

from a primary νέμω (to parcel out, especially food or grazing to animals); law (through the idea of prescriptive usage), genitive case (regulation), specially, (of Moses (including the volume); also of the Gospel), or figuratively (a principle)
KJV Usage: