i don't know all about them but a few are
1) What you are doing on one side do it on other side
eg -
x-10 = 5
x-10 + 10 = 5 + 10 [adding 10 on both the sides]
x= 15
or
10x = 100
10x/10 = 100/10
x = 10
or
x/ 10 = 10
x/10 * 10 = 10 * 10
x = 100
I hope you have understood