In this paper we will deal with the concept of unitary space and provide examples of operators in the unitary space, with special attention to unitary operators. Firstly, we will define the scalar product and the term unitary space. Some other basic concepts will be mentioned, (e.g. the norm and the orthonormal basis) needed to describe those operators. In the third chapter we will define unitary operators, specify their properties and give their characterization. Furthermore, we will list other examples of operators in the unitary space. Finally, we will define normal operators, which will unify the above-mentioned operators in the unitary space.