In this chapter we consider a bare homenegeous reactor, having an infinite cylinder geometry. At initial time, it will be assumed that a infinite line source emitting fission neutrons is introduced in the reactor. Our objective is to establish analytical equations describing the time dependant shape and magnitude of the thermal flux. The resolution of this problem combines the time-dependant diffusion equationDiffusionequationAgeequationHarmonic and the age equation, and will highlight the concept of harmonics and sheds new light on criticality. This chapter is inspired by the classical book of Lamarsh (Lamarsh in Introduction to nuclear reactor theory. Addison-Wesley Publishing Company, 1966, Chap. 9). At the end of the chapter, an overture is made to the question of reactor stability to xenon-induced oscillations, although this topic is not developed in this book.