An involution is a permutation such that its inverse is itself (i.e., cycle length less than 2). Due to this property involutions have been used in many applications including cryptography and coding theory. In this paper we provide a systematic study of involutions that are defined over finite field of characteristic 2. We characterize the involution property of several classes of polynomials and propose several constructions. Further we study the number of fixed points of involutions which is a pertinent question related to permutations with short cycle. In this paper we mostly have used combinatorial techniques.