A coalition is a group formed when two or more people, factions, states, political parties, militaries, or other parties agree to work together, often temporarily, in a partnership to achieve a common goal. The word coalition connotes a coming together to achieve a goal.
Coalitions manifest in a variety of forms, types, and terms of duration:
By contrast to alliances, coalitions are what might be termed "partnerships of unequals," since comparative political, economic, and military might, as well as the extent to which a nation is prepared to commit, dictates influence. Coalitions can often occur as an unplanned response to situations of danger, uncertainty, or extraordinary events, directed at interim objectives. 
Coalitions branch into two expanding categories: internal coalitions and external coalitions.
Internal coalitions consist of people who are already in an organization, such as a workplace. For example, a trade union is a type of coalition formed to represent employees' wages, benefits, and working conditions. Without this unity between employees, workers may be subjugated to harsh working environments and low pay due to no practical regulations. Often, organizations prefer to council with members of their respective internal coalitions before implementing changes at the workplace to ensure support.
In contrast, external coalitions consist of people that are members of different organizations who collaborate their efforts to achieve an overall objective. For example, in order to prevent gun violence and advocate gun control, several groups, unions, and nonprofit organizations banded to form the Coalition to Stop Gun Violence. External coalitions base their confidence in gaining credibility on inviting unlikely partners who wish to attain the same end goal, but the reasons to achieve these goals differ.
Coalition government is an alternative model to majoritarian governance, the latter being characterized by winner-take-all "first-past-the-post" electoral systems that favor clear distinctions between winners and losers. Not only can coalitions of legislative groups form governments in parliamentary systems but they can form in divisions of power as well. The most usual analyses of coalitions in politics deal with the formation of multiparty cabinets in parliamentary regimes. In Germany, every administration has been a multiparty coalition since the conclusion of the Second World War – an example of a coalition government creation in a parliamentary government. When different winning coalitions can be formed in a parliament, the party composition of the government may depend on the bargaining power of each party and the presence (or lack of it) of a dominant party.
The Cambridge Dictionary defines coalition as "the joining together of different political parties or groups for a particular purpose, usually for a limited time, or a government that is formed in this way".
The temporary collaboration of two or more separate parties with a set goal and common purpose can be viewed as a coalition in international relations. Coalition competitions are represented in international political dynamics . In international relations, a coalition can be an ad hoc grouping of nations united for specific purposes. Although persons and groups form coalitions for many and varied reasons, the most common purpose is to combat a common threat or to take advantage of a certain opportunity, resulting in the often temporary nature of coalitions. The common threat or existence of opportunity is what gives rise to the coalition and allows it to exist as all parties involved see the benefit in working together. Such collaborative processes allow the actors of the coalition to advance forward towards their overall goal or accomplish the task that the coalition was formed around. The behavior and dynamics of coalitions in international relations are created by commonalties and differences within the groups joining together. Rationality, group dynamics, and gender are all contributing factors of coalitional behaviors in an international security framework.
Economic agents can form coalitions. When a coalition is formed around economic goals, the reasoning is financial. In economics, when two opposing sectors such as a buyer and seller, or two sellers, come together it can be thought of as a coalition, in the denotative sense, as the two groups come together temporarily to achieve a goal. One example would be the 1997 deal between Microsoft and Apple. The deal consisted of Microsoft rescuing the then-struggling Apple with an infusion of $150 million. Unions can be viewed as coalitions of workers (usually of the same job sector). When the agents considered are countries, the formation of an international treaty (e.g. trade agreements or international environmental agreements) can also be seen as a coalition. In economics, a coalition's formation and its stability is mostly studied with tools from game theory.
In civil society, "coalition" connotes a group effort or a population of people coming together who believe strongly in their cause. The term also describes alliances between civil society organizations, such as labor unions, community organizations, and religious institutions. In France, for example, workers from different sectors and unions band together to aid each other in communicating a point. This coalition of unions is often very effective as it causes massive inconvenience to the country. The formation of coalitions such as the Community-Labor Coalition have proven to be an important strategy for social change in many contexts. In social groups, a coalition often forms from private citizens uniting behind a common goal or purpose. Many of these private citizen groups form grassroots organizations, such as the Christian Coalition, which is the largest grassroots political group in America. Activist groups in civil society are also viewed as coalitions for their respective cause. These activists are joined together by their belief in what they hope to achieve or accomplish.
Military coalitions can be built and united under a singular power by multiple states and governments. They are fluid in terms of membership—not only does a country not have to have been a traditional ally to join a coalition, but nations can join, vary their contributions and caveats, withdraw, and be replaced by new members as the situation changes or national agendas change. The expansion of assets accessible to member nations to perform military operations is a crucial attribute of coalitions. In many ways, coalition warfare serves to make the crafting of a peace more difficult than the winning of the war itself. An example of such a coalition happened during the Versailles Peace Conference in 1919 when the Allied powers attempted to reach a peace agreement.
Examples of military coalitions include the Coalition of the Gulf War, when George H. W. Bush ended Saddam Hussein's aggression in the Middle East by enlisting and leading a military coalition in the 1991 Gulf War's Operation Desert Storm as well as his son George W. Bush's efforts in the "Coalition of the Willing", a phrase employed during the 2003 campaign for the war in Iraq led by the United States and its allies. A contemporary example is the United Nations coalition that intervened in the 2011 Libyan Civil War against Muammar Gaddafi. For coalitions to be effective in principle or in action, participating nations have tended to require a single overpowering threat—perhaps to freedom or a way of life or a crucial national interest—or the presence of a single despotic figure or regime whose continued existence is considered not only abhorrent to the generality of nations but also destabilizing to the region or world order.
In mathematics, the term coalition is linked to an equation which uses the coalition model for exponential population growth. This analytical equation was first published by mathematician Pierre François Verhulst in 1838 to allow for the approximation of the world's population at a given time by applying differential and integral techniques.
The dictionary definition of coalition at Wiktionary