Quick simple (and probably not entirely correct) definitions:
 Prime  a prime number is a number which cannot be divided by any other numbers except itself or 1
 Modulo  in computation, it means that it returns the remainder of a number when it is divided by another
 Natural number  any negative or positive whole number
 Real number  in layman's terms, when you don't have a whole number
 Set  a group of numbers which could be generated by a generator for example
 Generator  every number is a generator; generates a group or set of integers
Main concepts
 Cannot divide numbers (otherwise a real number could result)
 Instead of dividing, a number can be inverted and multiplied
 Every number has an inverse
 Groups  are a set of integers, a set of mathematical operations and some rules which these numbers abide by
 A safe prime is a number where p is a prime and is the result of q (another prime) times 2 + 1 (p = 2q + 1)
 Order  Order of an element g (generator) is the smallest t such that g to the power of t = 1 mod p. In other words the values until 1 for that generator.
If we want to get the Order of all g's mod p (where p = 11), it will be one of { 1, 2, 5, 10 }

p  1 = 10 (if p is 11)

10 = 1 *10

10 = 2 * 5

10 = 10 * 1

10 = 5 * 2
Generate the below two tables for mod p using these programs (where p is a prime, is 11 and is also Safe).

./mult 11

1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 1 3 5 7 9

3 3 6 9 1 4 7 10 2 5 8

4 4 8 1 5 9 2 6 10 3 7

5 5 10 4 9 3 8 2 7 1 6

6 6 1 7 2 8 3 9 4 10 5

7 7 3 10 6 2 9 5 1 8 4

8 8 5 2 10 7 4 1 9 6 3

9 9 7 5 3 1 10 8 6 4 2

10 10 9 8 7 6 5 4 3 2 1


./exp 11

0 1 2 3 4 5 6 7 8 9 10

1 1 1 1 1 1 1 1 1 1 1 1

2 1 2 4 8 5 10 9 7 3 6 1

3 1 3 9 5 4 1 3 9 5 4 1

4 1 4 5 9 3 1 4 5 9 3 1

5 1 5 3 4 9 1 5 3 4 9 1

6 1 6 3 7 9 10 5 8 4 2 1

7 1 7 5 2 3 10 4 6 9 8 1

8 1 8 9 6 4 10 3 2 5 7 1

9 1 9 4 3 5 1 9 4 3 5 1

10 1 10 1 10 1 10 1 10 1 10 1
Okay, every number is a generator which generates a group of integers. Generation means taking a number (g) and raising it to a power.