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An Inquiry Concerning the Principles of Morals is a book by Scottish enlightenment philosopher David Hume. In it, Hume argues (among other things) that the foundations of morals lie with sentiment, not reason.
An Inquiry Concerning the Principles of Morals is the enquiry subsequent to the Inquiry Concerning Human Understanding. Thus, it is often referred to as "the second Inquiry". It was originally published in 1751, three years after the first Inquiry. Hume first discusses ethics in A Treatise of Human Nature (in Book 3 - "Of Morals"). He later extracted and expounded upon the ideas he proposed there in his second Inquiry. In his short autobiographical work, My Own Life (1776), Hume states that his second Inquiry is "of all my writings, historical, philosophical, or literary, incomparably the best."

Had every man sufficient sagacity to perceive, at all times, the strong interest, which binds him to the observance of justice and equity, and strength of mind sufficient to persevere in a steady adherence to a general and a distant interest, in opposition to the allurements of present pleasure and advantage; there had never, in that case, been any such thing as government or political society, but each man, following his natural liberty, had lived in entire peace and harmony with all others. What need of positive law where natural justice is, of itself, a sufficient restraint? Why create magistrates, where there never arises any disorder or iniquity? Why abridge our native freedom, when, in every instance, the utmost exertion of it is found innocent and beneficial? It is evident, that, if government were totally useless, it never could have place, and that the SOLE foundation of the duty of ALLEGIANCE is the advantage, which it procures to society, by preserving peace and order among mankind.

David Hume

The most important philosopher ever to write in English, David Hume (1711-1776) — the last of the great triumvirate of “British empiricists” — was also well-known in his own time as an historian and essayist. A master stylist in any genre, Hume's major philosophical works — A Treatise of Human Nature (1739-1740), the Enquiries concerning Human Understanding (1748) and concerning the Principles of Morals (1751), as well as the posthumously published Dialogues concerning Natural Religion (1779) — remain widely and deeply influential. Although many of Hume's contemporaries denounced his writings as works of scepticism and atheism, his influence is evident in the moral philosophy and economic writings of his close friend Adam Smith. Hume also awakened Immanuel Kant from his “dogmatic slumbers” and “caused the scales to fall” from Jeremy Bentham's eyes. Charles Darwin counted Hume as a central influence, as did “Darwin's bulldog,” Thomas Henry Huxley. The diverse directions in which these writers took what they gleaned from reading Hume reflect not only the richness of their sources but also the wide range of his empiricism. Today, philosophers recognize Hume as a precursor of contemporary cognitive science, as well as one of the most thoroughgoing exponents of philosophical naturalism.