Adultery is very realted to the covenant of marriage. If a person is under the covenant of marriage, and sleeps outside of that covenant of marriage, then that person commits adultery sinning against his/her spouse and their covenant of marriage.
In the ancient Near-East, biblical days, most couples established marriage covenants that expected women to be reserved for their husband, but men were not expected to either not take another wife or be intimate with a single woman. This was the norm, but not the rule; some couples agreed upon a covenant of marriage that established the family in monogamy and both the man and woman agreed to be faithful to each other and not be physically intimate with anyone but their spouse.
In our culture today, most marriage covenants are entered with the expectation of mutual faithfulness, and thus for a married person, husband or wife, to be sexually intimate with someone other than one's spouse is to commit adultery and sin against one's self, one's spouse, against the marriage covenant, and against God!
Concerning the role of civil government, I believe that civil governments are established by God to bring social order, to mitigate the oppression of the weak, and to protect it's members. Part of fulfilling these responsibilities means that the civil government much enact and enforce laws restraining the selfishness of mankind. Should civil government penalize adultery. Apparently God thinks so for He inspired Moses to legislate civil law for the nation of Israel that penalized adultery with capitol punishment, death by stoning. Adultery was thus a serious offence against not only one's spouse but apparently against the social order.
Of course, speaking prophetically of issues of the heart, Jesus challenged us to be careful not to lust/covet after someone else's wife. And Paul goes on to encourage, especially young men, to flee fornication. We can become so consumed with our selfish physical desires that we'll eventually sin and bring destruction into our lives and the lives of others.
Jesus also endoresed monogamy as the divine ideal for marriage, and frankly, the further we get away from the divine ideal, the more problems we'll have and our loved ones will have. But did God inspire Moses to legislatively enact monogamy? No. Should our government legislate monogamy? I'm not firmly convinced either way.