Numbers
In Decimal number system, there are ten symbols namely 0,1,2,3,4,5,6,7,8 and 9 called digits. A number is denoted by group of these digits called as numerals.
Face Value
Face value of a digit in a numeral is value of the digit itself. For example in 321, face value of 1 is 1, face value of 2 is 2 and face value of 3 is 3.
Place Value
Place value of a digit in a numeral is value of the digit multiplied by 10ⁿ where n starts from 0. For example in 321:

Place value of 1 = 1 x 10⁰ = 1 x 1 = 1
Place value of 2 = 2 x 10¹ = 2 x 10 = 20
Place value of 3 = 3 x 10² = 3 x 100 = 300
0^th position digit is called unit digit and is the most commonly used topic in aptitude tests.
Types of Numbers
Natural Numbers - n > 0 where n is counting number; [1,2,3...]
Whole Numbers - n ≥ 0 where n is counting number; [0,1,2,3...].
0 is the only whole number which is not a natural number.
Every natural number is a whole number.

Integers - n ≥ 0 or n ≤ 0 where n is counting number;...,-3,-2,-1,0,1,2,3... are integers.

Positive Integers - n > 0; [1,2,3...]
Negative Integers - n < 0; [-1,-2,-3...]
Non-Positive Integers - n ≤ 0; [0,-1,-2,-3...]
Non-Negative Integers - n ≥ 0; [0,1,2,3...]

1. 0 is neither positive nor negative integer.

Even Numbers - n / 2 = 0 where n is counting number; [0,2,4,...]
Odd Numbers - n / 2 ≠ 0 where n is counting number; [1,3,5,...]

Prime Numbers - Numbers which is divisible by themselves only apart from 1.
1 is not a prime number.
To test a number p to be prime, find a whole number k such that k > √p. Get all prime numbers less than or equal to k and divide p with each of these prime numbers. If no number divides p exactly then p is a prime number otherwise it is not a prime number.

Composite Numbers - Non-prime numbers > 1. For example, 4,6,8,9 etc.

1 is neither a prime number nor a composite number.

2 is the only even prime number. 

Co-Primes Numbers - Two natural numbers are co-primes if their H.C.F. is 1. For example, (2,3), (4,5) are co-primes.

Some Basic Formulae:

1. (a + b)(a - b) = (a² - b²)
2. (a + b)² = (a² + b² + 2ab)
3. (a - b)² = (a² + b² - 2ab)
4. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
5. (a³ + b³) = (a + b)(a² - ab + b²)
6. (a³ - b³) = (a - b)(a² + ab + b²)
7. (a³ + b³ + c³ - 3abc) = (a + b + c)(a² + b² + c² - ab - bc - ac)
8. When a + b + c = 0, then a³ + b³ + c³ = 3abc.