  The study of computability has its origin in Hilbert's conference of 1900,
where an adjacent question, to the ones he asked, is to give a precise
description of the notion of algorithm. In the search for a good definition
arose three independent theories: Turing and the Turing machines, G\"odel and
the recursive functions, Church and the Lambda Calculus.
  Later there were established by Kleene that the classic models of computation
are equivalent. This fact is widely accepted by many textbooks and the proof is
omitted since the proof is tedious and unreadable. We intend to fill this gap
presenting the proof in a modern way, without forgetting the mathematical
details.
