In mathematics, a number system refers to a set of mathematical symbols and rules that allow us to represent, manipulate, and perform arithmetic operations on numbers. A number system consists of a set of digits or symbols used to represent the numbers and a set of rules that define how to perform basic arithmetic operations, such as addition, subtraction, multiplication, and division.

For example, the decimal number system, which is the most commonly used number system, uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) and the place value system to represent numbers. Similarly, there are other number systems such as binary, octal, hexadecimal, and more. Each number system has its own set of digits and rules for representing and manipulating numbers. The choice of number system depends on the application and the requirements of the problem at hand.

The chapters or topics covered in the number system in mathematics may vary depending on the level of study. However, here are some of the common topics that are typically covered:

- Integers
- Rational Numbers
- Irrational Numbers
- Real Numbers
- Complex Numbers
- Decimal System
- Binary System
- Octal System
- Hexadecimal System
- Number Bases and Conversions
- Place Value
- Number Theory
- Prime Numbers
- Composite Numbers
- Factors and Multiples
- Divisibility Rules
- GCD (Greatest Common Divisor)
- LCM (Least Common Multiple)
- Euclid’s Division Lemma
- Euclid’s Algorithm
- Modular Arithmetic
- Congruence
- Diophantine Equations
- Fermat’s Little Theorem
- Euler’s Totient Function
- Number Patterns and Sequences.

These are some of the topics that are commonly covered in the number system in mathematics.