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In simple words, Equity is a set of principles (not rules) developed from the discretionary judgement of judge in the Court of Chancery. It is an ad hoc exercises of judge's power to do justice in individual cases. And there is no binding principle here.
Equity acts in personam, that equity does not determine rights under law, rather it requires particular individuals to act according to conscience.
Historically, equity and common law were dealed with under separated courts. But now they are united in a single one. Litigants can now seek rememdy under equity and common law in the same court.
Equity principles governs entirely the Law of Trusts (express trusts, constructive trusts and resulting trusts) and some part of Law of Contract (promissory estoppel). While Common Law deals with all other remaining part of the legal system.
Some one has asked about the stare decisis, I believe the answers are in the textbook. Please do take some time to read before you ask someone for an essay.