Abstract
These are a set of notes on the Class Number in Number Theory. We prove Fermat's theorem on sum of two squares for primes of the form 4k+1. We also prove Dirichlet's Divisor theorem and Voronoi's improvement. Lastly we prove the theorem of Rabinovitch, on polynomials that taken on prime values, which is related to the characterization of discriminants which have class number 1.