  Let $A$ be a set of natural numbers. A set $B$, a set of natural numbers, is
said to be an additive complement of the set $A$ if all sufficiently large
natural numbers can be represented in the form $x+y$, where $x\in A$ and $y\in
B$. This article describes various types of additive complements of the set $A$
such as those additive complement of $A$ that does not intersects $A$, additive
complements of the form of the union of disjoint infinite arithmetic
progressions, additive complement having various density etc. As an application
of this study, we also focus on the structure of sumset of arithmetic
progression and geometric progression. Apart from this, for given positive real
no. $\alpha \leq 1$ and finite set $A$, we investigate a set $B$ such that it
can be written as union of disjoint infinite arithmetic progression and density
of $A+B$ is $\alpha$.
