Liberalism is a philosophical, political and economic theory, and ideology that emanates from the position that individual freedoms are the legal basis of society and economic order.
The ideal of liberalism is a society with freedom of action for everyone, free exchange of politically sensitive information, limiting the power of church and state, rule of law, private property and freedom of private enterprise.  Liberalism rejected many of the provisions that were the basis of previous theories of the state, such as the divine right of kings to rule and the role of religion as the sole source of knowledge. Fundamental principles of liberalism include the recognition: data on the nature of natural rights (including the right to life, liberty and property), as well as other civil rights; equity and equality before the law; market economy; government’s responsibility and transparency of government. 3

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The function of the government is reduced to the minimum necessary to ensure these principles.  Modern liberalism also prefers an open society based on pluralism and democratic government, while protecting minority rights and individual citizens. Some modern trends of liberalism are more tolerant of government regulation of free markets for the sake of equal opportunity to succeed, universal education and reducing the difference in incomes.  Proponents of such views believe that the political system should contain elements of the welfare state, including state unemployment benefits, homeless shelters and free health care. According to the views of liberals, government exists for the benefit of the people subservient to it, and the country’s political leadership should be based on the consent of the majority of the led.  To date, the political system, which is most consonant with the beliefs of liberals, is liberal democracy.
Nowadays, liberalism is one of the leading ideologies in the world.  The concept of personal liberty, dignity, freedom of speech, universal human rights, religious tolerance, privacy, private property, free markets, equality, rule of law, government transparency, limits on state power, the supreme power of the people, self-determination of the nation, enlightened and sound public policy – are commonplace. For the liberal-democratic political systems countries are so different in culture and level of economic well-being, such as Finland, Spain, Estonia, Slovenia, Cyprus, Canada, Uruguay and Taiwan.  In all these countries, liberal values play a key role in shaping the new society’s goals, even though the gap between ideals and reality.
The following list of current political trends within liberalism is in no way not exhaustive.  By virtue of the fact that in Western Europe and North America, most political movements are in solidarity with the ideals of political liberalism, there was the need for a more narrow classification.  The right-wing liberals have focused on classical liberalism, but objected to several provisions of social liberalism.  They adjoin the conservatives who share and become traditional in these countries, political liberal values, but frequently condemn some of the cultural manifestations of liberalism as contrary to morality.  It should be noted that, historically, conservative liberalism is an ideological antagonist, but after the Second World War and the discrediting of authoritarian leadership role in the western conservatism began to play a moderate flow (Liberal conservatism, Christian Democracy).  In the second half of XX century the Conservatives were the most active defenders of private property and the supporters of privatization. Libertarians believe that government should not interfere in personal life or business, except to protect the liberty and property of some of the encroachments of others. They support the economic and cultural liberalism and oppose social liberalism.  Part of the libertarian believes that for the implementation of rule of law, the state must have sufficient strength; others argue that law enforcement should be carried out by public and private organizations.  In foreign policy, libertarians generally are opposed to any military aggression. 4
Modern social liberals tend to regard themselves as centrists and Social Democrats. Considerable influence, recently gained in particular in Scandinavia, where a series of protracted economic decline, has exacerbated social security (unemployment, pensions, inflation).  To solve these problems, the Social Democrats have been steadily increasing taxes and public sector in the economy.   However, many decades of hard struggle for power between the right and other liberal forces led to the effective laws and transparent government, which effectively protect the civil rights of persons and property of entrepreneurs.  Attempts to divert the country too far toward socialism led to the Social Democrats in the loss of power and the subsequent liberalization.  So today, in the Nordic countries prices are not regulated (even state-owned enterprises, with the exception of monopolies), private banks, and there are no barriers to trade, including international.  This combination of liberal and social policies led to the realization of liberal-democratic political system with a high level of social protection. 
The main objectives of its policy of liberal parties most often is considered the strengthening of liberal democracy and the rule of law, judicial independence, control over the transparency of government, civil rights and free competition.  However, the presence of the word “liberal” in the name of the party itself cannot determine whether her right-wing supporters of the liberals, social liberals or libertarians.
Public liberal movements also vary significantly.  Some movement in favor of sexual freedom, free sale of weapons or drugs, the expansion of the functions of private security firms and the transfer of part of the police.  Economic liberals often favor a single rate of income tax, or even replace the income tax per capita, for the privatization of education, healthcare and public pension system, for the translation of science to finance the self-supporting.  In many countries, the liberals are in favor of abolition, disarmament, renunciation of nuclear technology and environmental protection. In recent years, the debate over multiculturalism has intensified.  While all parties agree on the fact that ethnic minorities should share the fundamental values of society, some believe that the function of the majority should be limited to protecting the rights of ethnic communities, while others are proponents of early integration of minorities in the name of preserving the integrity of the nation.
Marxism is the philosophical, political and economic doctrine and a movement founded by Karl Marx in the middle of the XIX century.  There are different interpretations of Marx’s theory of the different political parties and movements in social thought and political practice.  Political Marxism is a version of socialism, along with left-anarchism, Christian socialism and Marxism is not the host part of the Democratic Socialism / Social Democracy. 1
Traditionally it is believed that the importance of Marx’s theory is the following: the doctrine of surplus value, the materialist conception of history (historical materialism) and the doctrine of the dictatorship of the proletariat. Often it is divided: Marxism as a philosophical doctrine (dialectical and historical materialism); Marxism as a doctrine that has had an impact on scientific concepts in economics, sociology, political science and other sciences; Marxism as a political movement, asserting the inevitability of class struggle and social revolution, and the leading role of the proletariat in the revolution that will lead to the destruction of commodity production and private property, which form the basis of capitalist society and the establishment on the basis of public ownership of means of production of a communist society which aims the development of each member of society.
In his early works, Marx on the one hand condemns the philosophy behind its contemplative consciousness, but on the other hand, strongly emphasizes the need to translate the philosophy into reality.  Thus, the widely known 11-th Marx’s thesis on Ludwig Feuerbach: “Philosophers have only interpreted the world in different ways, but the point is to change it”.
Later this position degenerates into a sharp criticism of metaphysical philosophy in The German Ideology. 2
In some countries during some historical periods in power, there were various political parties and movements who called themselves Marxist, or were influenced by Marxism. Marxism in these countries is often declared as the official state ideology or that of a de-facto.
Not all policies were used and are still using Marxism to justify their actions, actually it was disassembled and its consistent and has strong supporters.  Quite often Marxism is used as an ideological cover for plans and actions, far from the ideas and goals of Marxism. Several modern scholars have expressed the view that the Soviet Union and certain other countries party nomenclature used Marxist ideas in their dogmatized and vulgar representation.
All in all, the ideas of Liberalism and Marxism are incompatible in contemporary forms of political governance because both Liberalism and Marxism were created at the time when they were indispensable, when it was worth to try these ideas, to implement them and to study them as well. Although for some people these ideas seem to be optimistic and promising, for the modern world and economy, these ideas are morally old and they are not valuable for majority of the countries, because the world have changed, the principles have changed and capitalism is the most efficient and modern system of the current way of life that fits the society. Anyway, both Liberalism and Marxism had the same goals- to help the society live better, using their own principles, vision and ideas and proposing them as the best way out of problems. These ideas cannot be reconciled in any way, but some ideas from them can be depicted when creating a new approach that will be effective for the economy. Implementing these ideas into the modern society and the modern world would be unreal and very risky.