Classical Theory of Fourier Series:Demystified and Generalised
  For a Riemann integrable function on an interval and for a point therein,we define 'Fourier series at the point on the interval' and bring out how and when the function element becomes expressible as Fourier series.In this process,we also generalise the theory by bringing in such concepts as finite Fourier series,right/left hand Fourier series.We also sum up subseries corresponding to terms in an arithmetic progression,of the basic Fourier series. 
Vivek V. Rane