Sure the three main notations are:
"Big-Oh" meaning your function is always <= c*f(x) for some constant c and values greater than some x.
"Big-Omega" meaning your function is always >= c*f(x) for some constant c and values greater than some x
"Big-Theta" which is used to describe a tight upper and lower bound, meaning it is both Big-Oh and Big-Omega. To show Big-Theta you should show both Big-Oh and Big-Omega are the same.
And then on top of all this sometimes you will hear about the "worst case of the best case" or "best case of the worst case" etc.
And to the person above who talks about quick sort, what about smooth sort?