That branch of mathematics which treats of the relations and properties of quantity by means of letters and other symbols. It is applicable to those relations that are true of every kind of magnitude.

A treatise on this science.

A branch of mathematics in which variables are substituted for unknown values to solve a particular problem.

A branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale, what is done on one side of the scale with a number is also done to the other side of the scale. The numbers are the constants.

a formal structure consisting of sets and operations on those

a set of objects (called Set here) plus other documentation (named DOC here) defining constants, operations and axioms

a set with a system of operations defined on it