War is a game mechanic where corporations and/or alliances can fight in hisec space without CONCORD intervention or security status loss.
War Declaration Mechanics ('Deccing')
To initiate war, a corporation has to pay a fee to CONCORD (essentially a bribe). To declare war on another corp you must have the director or CEO role in your current corporation, you must then cast a vote from the politics tab of the corp menu to declare war on the desired corporation. Once the vote has been returned with majority yes vote (the minimum voting period is 24 hours) the ceo may put the war into effect from the sanctionable actions tab.
For an alliance, the process is different. The CEO or a director of the Executor Corp must open the Corporation interface, go to the Alliances tab, then view the "Home" tab. At the bottom of the window is button labelled "Declare War." The CEO must push the button and enter the name of the target corporation or alliance, then press search. Once he or she has confirmed the selected alliance is the correct one, war is immediately declared, with fighting becoming possible after a 24 hours notice period.
Once war is declared, there is a 24-hour startup period where fighting cannot occur, to give both sides a chance to get ready for the war. Once the war is active, there will be a period of one week where any aggression can occur between the two sides without CONCORD intervention. A corporation can only issue a maximum of 3 wardecs; an alliance has no such limit.
- How much does a wardec cost ? (as of 2012.05.14)
- It costs at least 50 million isk for a corporation to declare war on another corporation.
- The war declaration fee must be in the Master Wallet of the corp wallet.
The formula for calculating wardec cost is (log2.05831 N)^2 * 300000 * N^0.27, where N is the number of corp members. The cost is now the same when declaring on a corporation or an alliance. 
This base-cost can be increased by the number of wars you currently have ongoing (where you are the aggressor) and the number of wars the target corporation already has against them. The formula for calculating the cost is B * (N +1) * (W + 1). Where B = Base Price, N = number of wars you currently have, W = number of wars currently against the target corporation. Mutual wars are not considered in the cost calculation.
If the receiver of the wardec chooses, they can make the war dec mutual. Mutual wars do not cost the aggressor the usual war weekly fee and won't expire unless the war is manually retracted or the mutual status is revoked. Mutual wars also do not increase the cost of declaring war on other organizations or the cost of an organization declaring war upon your organization.
Ending the War
Wars can end in one of several ways. If the week ends without a renewal fee paid for the war, then CONCORD will declare the war invalid. The CEO of the aggressor corporation can decide to end the war at any time. Finally, the war can be surrendered by the defending corporation's CEO. The two CEOs have to meet in the same station, and a trade window will allow goods to be exchanged in return for the end of the war.
Whichever way a war ends, there will be a 24 hour cooldown period where fighting can still occur. This prevents ending a war to avoid a particular engagement. After this cooldown, normal CONCORD services will resume.
University Rules during War
The University has a different set of rules during war, designed to make conflicts as un-fun as possible for the aggressors, and to reduce the number of wardecs that the University receives. Probably the most important page to read is the Wartime SOP and the reasons for it. Listening to a War 101 class and browsing the rest of the wiki is highly recommended.
How to Check the Status of a War
Open the corporation window in your NeoCom and select the Wars tab. Note that fighting can occur 24 hours after the war started and 24 to 25 hours after it is finished (the 'can fight' column shows, if the war is live).