To get the appearance of the entries in the references, keep using the plainnat bibliography style but do not load the natbib package. You'll get:



\documentclass[a4paper]{article} % to keep output all on one page
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amssymb,amsthm,graphicx}
%\usepackage{natbib} %% deliberately commented out
\bibliographystyle{plainnat}
\usepackage{filecontents}
\begin{filecontents*}{Ref.bib}
@book{alp:04,
  author   = "Ethem Alpaydin", 
  title    = "Introduction to Machine Learning",
  publisher= "MIT Press",
  year     = 2004,
}
\end{filecontents*}
\begin{document}
\cite{alp:04}
\bibliography{Ref}
\end{document}




If you do not want square brackets surrounding the citation callout, i.e., if you want it to look like Alpaydin(2004), you should also provide the following instructions in the preamble:

\usepackage[noadjust]{cite}
\renewcommand\citeleft{}
\renewcommand\citeright{}




If you did load natbib -- and, of course, didn't load the cite package as well -- you'd get the following look, which is, I gather, not what you want:



Referencing (not Bibliography) in Harvard Style using Write Latex
Who were the "Prophets of Zwickau" and what influence did they have on modern Christianity?  

I'm interested in their theology, history, and influence on Christianity in their day, and whether or not their influence continues to today.  
