Classical liberalism is a political tradition and a branch of liberalism that advocates free market and laissez-faire economics; civil liberties under the rule of law with especial emphasis on individual autonomy, limited government, economic freedom, political freedom and freedom of speech.
Classical liberalism is a philosophy of individualism and self-responsibility with little concern for groups or sub-communities. Classical liberals in the United States believe that if the economy is left to the natural forces of supply and demand, free of government intervention, the result is the most abundant satisfaction of human wants.
Classical antiquity is a broad term for a long period of cultural history. Such a wide sampling of history and territory covers many rather disparate cultures and periods. "Classical antiquity" often refers to an idealized vision of later people, of what was, in Edgar Allan Poe's words, the glory that was Greece, the grandeur that was Rome!
John Stuart Mill contributed enormously to liberal thought by combining elements of classical liberalism with what eventually became known as the New Liberalism. Mill's 1859 On Liberty addressed the nature and limits of the power that can be legitimately exercised by society over the individual . 
The diversity of liberalism can be gleaned from the numerous qualifiers that liberal thinkers and movements have attached to the term "liberalism", including classical, egalitarian, economic, social, the welfare state, ethical, humanist, deontological, perfectionist, democratic and institutional, to name a few.
As such, economic liberalism today is associated with classical liberalism, neoliberalism, right-libertarianism, and some schools of conservatism like liberal conservatism and fiscal conservatism. Economic liberalism follows the same philosophical approach as classical liberalism and fiscal conservatism.
Because liberty was an important part of republican thought, many republican thinkers were appropriated by the theory of classical liberalism. Classical republicanism became extremely popular in Classicism and during the Enlightenment , playing a central role in the thought of political philosophy since Hobbes , through John Locke , Giambattista Vico , Montesquieu , Rousseau , until Kant .