Where could I find a detailed exposition in English of Godel's proof (not Henkin's) of Completeness Theorem for first order logic? The wikipedia article omits certain details that I am not clear about, and Godel's original dissertation is not in English.

4$\begingroup$ global.oup.com/academic/product/… $\endgroup$ – Andrés E. Caicedo Mar 6 '16 at 20:37

1$\begingroup$ If you are interested in a text book treatment which leads you from the basics to a proof of Gödel's theorem, then I can highly recommend "Mathematical Logic" by Shoenfield which was (is ?) the standard graduate text on the subject of its title. $\endgroup$ – oeiras Mar 10 '16 at 17:36

$\begingroup$ @oeiras: The proof of completeness given by Shoenfield is the one due to Henkin, which is not what the questioner wants. $\endgroup$ – Philip Ehrlich Mar 14 '16 at 0:23
In addition to an English translation of the original version contained in the Collected Works referred to by Andrés, there is an English translation of a rewritten version of the paper contained in From Frege to Gödel edited by Jean van Heijenoort. The latter is also contained in the Collected Works.