The Dempster-Shafer theory of evidence is developed in a very general setting. Its algebraic part is discussed as a body of arguments which contains an allocation of support and an allowment of possibility for each hypothesis. A rule of combination of bodies of arguments is defined which constitutes the symbolic counterpart of Dempster's rule. Bodies of evidence are introduced by assigning probabilities to arguments. This leads to support and plausibility functions on hypotheses, which constitute the numerical part of evidence theory. Combination of evidence based on the combination of bodies of arguments is discussed and Dempster's rule is derived.