Algebra is a subject that studies numbers, quantities, relationships and structures, and has important applications in many fields. The following are some major application areas:

1. Physics: Algebra is widely used in physics, including mechanics, electromagnetism and quantum mechanics. For example, Newton's laws of motion are described by algebraic equations.

2. Engineering: In engineering, algebra is used to design and analyze various systems, such as circuits, mechanical systems and building structures.

3. Computer Science: In computer science, algebra is used to design and analyze algorithms and to process data and information. For example, linear algebra is widely used in graphics, machine learning and other fields.

4. Economics: In economics, algebra is used to establish and solve various economic models, such as supply and demand model and production function model.

5. Statistics: In statistics, algebra is used to establish and solve various statistical models, such as regression models and variance analysis models.

6. Biology: In biology, algebra is used to establish and solve various biological models, such as genetic models and ecological models.

7. Social science: In social science, algebra is used to establish and solve various social models, such as population model and social network model.

8. Cryptography: In cryptography, algebra is used to design and analyze various encryption algorithms.

9. Finance: In finance, algebra is used to establish and solve various financial models, such as option pricing model and risk management model.

Generally speaking, algebra is a basic tool in many fields and is widely used.