The best renormalizable theory in particle physics is the Standard Model. According to this model, neutrinos must be massless. We know that neutrinos have three different flavors. Owing to the observations, it is seen that there are oscillations between different flavors of neutrinos. This fact forces us to go beyond the Standard Model of Particle Physics, because neutrino oscillations can only happen if the neutrinos are massive. The first solution is to define three mass eigenstates and claim that the flavor eigenstates are superpositions of the mass eigenstates.
However, due to some problems it is concluded that physical states must be replaced with fields. In this thesis we study neutrino oscillations. We begin our work with reviewing fermion fields before the Standard Model. Then the Standard Model and experiments which confirm the existence of different neutrino flavors are shortly discussed. Moreover, we present the observations that show neutrino oscillations phenomenon and after that, the Dirac and Majorana neutrinos are discussed. Finally, oscillations are described theoretically. First, quantum mechanical oscillations are discussed and we find the phase and probability of the flavor transitions. Then due to the problems of this approach, oscillations in quantum field theory are presented. It is seen that, again, the results derived with the quantum mechanical treatment are accepted in the quantum field theory approach.
