There are various types and properties of integers that can be explained in detail.

1. Whole Numbers:
- Whole numbers include all the positive integers (1, 2, 3, ...) and zero (0).
- They do not include any negative numbers.

2. Positive Integers:
- Positive integers are all the whole numbers greater than zero.
- They do not include zero or any negative numbers.

3. Negative Integers:
- Negative integers are all the whole numbers less than zero.
- They do not include zero or any positive numbers.
- Negative integers are denoted with a negative sign (-) before the number.

4. Zero:
- Zero is a special integer that represents the absence of quantity or value.
- It is neither positive nor negative and is denoted by the number 0.

5. Opposites or Additive Inverses:
- Every integer has an opposite or additive inverse.
- The opposite of a positive integer is a negative integer with the same magnitude.
- The opposite of a negative integer is a positive integer with the same magnitude.
- The sum of an integer and its opposite is always equal to zero.

6. Absolute Value:
- The absolute value of an integer is its distance from zero on the number line.
- It is always a positive value or zero.
- The absolute value of a positive integer is the number itself.
- The absolute value of a negative integer is the number without its negative sign.

7. Ordering Integers:
- Integers can be arranged in a number line from least to greatest or vice versa.
- The greater the integer, the farther it is from zero.
- The lesser the integer, the closer it is to zero in the negative direction.

8. Operations on Integers:
- Integers can be added, subtracted, multiplied, and divided.
- When adding or subtracting integers, the signs of the numbers determine the result.
- When multiplying or dividing integers, the signs of the numbers determine the result as well as the sign of the answer.

By understanding these different types and properties of integers, you can work with them effectively in various mathematical operations and problem-solving.