Communism is a revolutionary socialist movement to create a classless, moneyless and stateless social order structured upon common ownership of the means of production, as well as a social, political and economic ideology that aims at the establishment of this social order. This movement, in its Marxist–Leninist interpretations, significantly influenced the history of the 20th century. Marxist theory holds that pure communism or full communism is a specific stage of historical development that inevitably emerges from the development of the productive forces that leads to a superabundance of material wealth, allowing for distribution based on need and social relations based on freely associated individuals.
Source: http://en.wikipedia.org/wiki/Communism
Federal Republic
A federal republic is a federation of states with a republican form of government. Usage of the term republic is inconsistent but, as a minimum, it means a state or federation of states that does not have a monarch.
In a federal republic, there is a division of powers between the national government, and the government of the individual subdivisions. While each federal republic manages this division of powers differently, national security and defense, monetary policy, and other issues of a "national" scope are handled at the "federal" level while more local issues such as road and infrastructure maintenance and education policy are handled at the local level
Theocratic republic is a form of government in which a deity is officially recognized as the civil Ruler and official policy is governed by officials regarded as divinely guided, or is pursuant to the doctrine of a particular religion or religious group. From the perspective of the theocratic government, "God himself is recognized as the head" of the state, hence the term theocracy, from the Greek θεοκρατία "rule of God". In a pure theocracy, the civil leader is believed to have a direct personal connection with God.
Source:
http://en.wikipedia.org/wiki/Theocracy
http://www.blurtit.com/q140529.html
http://en.wikipedia.org/wiki/Islamic_republic
Monarchy
A monarchy is a form of government in which sovereignty is actually or nominally embodied in a single individual - the monarch.
Forms of monarchy differ widely based on the level of legal autonomy the monarch holds in governance, the method of selection of the monarch, and any predetermined limits on the length of their tenure. When the monarch has no or few legal restraints in state and political matters, it is called an absolute monarchy and is a form of autocracy. Cases in which the monarch's discretion is formally limited (most common today) are called constitutional monarchies.
Source: http://en.wikipedia.org/wiki/Monarchy
Republic
A republic is a form of government in which the country is considered a "public matter", not the private concern or property of the rulers, and where offices of state are subsequently directly or indirectly elected or appointed rather than inherited. In modern times, a common simplified definition of a republic is a government where the head of state is not a monarch. Both modern and ancient republics vary widely in their ideology and composition.
In modern republics such as the United States, France, Russia, India, and Mexico the executive is legitimized both by a constitution and by popular suffrage.
Source: http://en.wikipedia.org/wiki/Republic
Democracy
Democracy is a form of government in which all eligible citizens have an equal say in the decisions that affect their lives. Democracy allows eligible citizens to participate equally—either directly or through elected representatives—in the proposal, development, and creation of laws. It encompasses social, economic and cultural conditions that enable the free and equal practice of political self-determination. A democratic government contrasts to forms of government where power is either held by one, as in a monarchy, or where power is held by a small number of individuals, as in an oligarchy.