Lecture on Fourier Series: 1. Why Fourier is possible? 2. Why Fourier series is plausible? 3. What is the Fourier series actually? 4. Why is Fourier series useful? Why Fourier series possible? We first begin with a few basic identities on the size of sets. Show that the set of possible functions representing sets is not larger than the set of available functions? Why Fourier series is plausible?