Algebraic systems are mathematical structures that consist of a set of elements and operations defined on those elements. Common examples include groups, rings, and fields, each with specific properties and rules. These systems help mathematicians understand and solve equations and relationships in a structured way. In an algebraic system, operations like addition and multiplication can be performed, and they follow certain axioms or rules. For instance, in a group, the operation must be associative, and there must be an identity element. Understanding these systems is essential for advanced mathematics and applications in various fields, including physics and computer science.