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Common Law is the body of law developed from custom or judicial decisions in English and U.S. courts, not attributable to a legislature. Which means that it is a system in which principles are developed based on past situations with similar conditions. In this sense common law is founded on the precedence of first occasions. In the case of an event that an instance has never before happened the outcome of this event sets the precedent for futher cases.
American law is based on federal and state constitutions. The Constitution of The United States is considered to be the supreme law of the land and no law can supersede that law. The Constitution sets the guidelines for all law in the states. This also deems for laws within states the law of the states are considered to be the law of that particular state, and is the law their unless deemed un-constitutional by the Constitution.
The importance of precedent in the judicial decision making process is that laws and past cases can be examples in decisions to be made. The relevance in legal principles is what makes things related in a legal process and helps influence decisions and which makes this process work.
Equitable remedies are a branch of law founded on notions of justice and fair dealing. This supplies a remedy when there is not a adequate remedy available. While a legal remedy is when a court of law exercises the law and enforces the right and orders the penalty.