Liberalism: A a diverse political Ideology which values liberty and equality, in various senses of the words.
Modern American Liberalism: Often associated with or aligned with socialism and progressivism, liberty and equality are of the stressed values, where liberty is a relative freedom of autonomy, less so with respect to the government. In order to improve the situation of the less privileged, those with more privilege in any given area may be taxed and regulated more strictly, and those with less privilege in that same area may be granted more entitlements or breaks. This is known as equality of outcome and equality of status over equality of the law. All people have the right to be provided with entitlements through the methods outlined above. Important thinkers include Lyndon B. Johnson, H. L. A. Hart, Franklin D. Roosevelt (of the New Deal), and John Rawls (The Great Society programs).
Modern European Liberalism: A centrist political party, unaffiliated with socialism, that supports a long legacy of individual liberty and constitutionally constrained, democratically accountable government. This also involves, albeit to a lesser extent, the employment of progressive measures to improve the lot of society's underprivileged members without fundamentally altering it. Canada's liberalism more accurately reflects the European tradition than the American.
The level of government interference in the economy is a contentious issue among European liberals, although generally speaking, they support moderate intervention. Today, the majority of liberal parties in Europe follow conservative liberalism's tenets, like the Canadian Liberal Party; just a small number follow social liberalism's tenets, like the British Liberal Democrats.
Classical Liberalism: The political philosophy which began in the enlightenment stressing individual liberty and equality under the law as absolutes. This often takes the form of a limited constitutional republic that upholds a mostly free market and defends the inherent rights of Life, Liberty, and Property as understood by its leading philosophers. (Property as in the defense of individual property rights; not as in the sharing of property.) The definition of liberty, according to the popular usage of the word, is the ability to act without causing harm to another, whereas the definition of equality is to be treated equally under the law regardless of one's standing or advantage. Major thinkers include John Locke, John Stuart Mill, Thomas Jefferson, Thomas Paine... I really could go on.
Neoliberalism: The term "neoliberalism" refers to economic liberalism, and its proponents favor economic liberalization, free trade, open markets, privatization, deregulation, and strengthening the private sector's position in contemporary society. However, it is not a fair or conventional approach to the market; rather, it is a compromise between the former and central planning. It maintains the major components of the market of a classical liberalism while introducing the social programs characteristic in Modern American Liberalism. Major thinkers include Fredrick Hayek and Milton Friedman.