Notations

The most common notations used in the theory of algorithms are $\Theta (N)$, $O(N)$, $\Omega (N)$.

Big Theta $\Theta (N)$ Notation

$\Theta (N)$ is usually implied any time Asymptotic Order of growth or any analogue is used. Note: This explicitly includes situations such as worst case Asymptotic runtime, etc.

It is primary used to classify algorithms and provides a running time estimation, not a bound.

Big Oh $O(N)$ Notation

$O(N)$ provides an upper bound to the run time of an algorithm.

It states that this algorithm must run in $\Theta (N)$ or less time.

It is commonly used for worst case running time.

Big Omega $\Omega (N)$ Notation

$\Omega (N)$ provides a lower bound to the run time of an algorithm.

It states that this algorithm must run in $\Theta (N)$ or more time.

It is commonly used for best case running time.