I can't fully reproduce your output since I don't have the image1 graphic. I'd like to make the following suggestions, though:
Insert a \noindent directive immediately before the first \begin{wrapfigure} statement.
Don't leave blank lines between the three wrapfigures. Remember: when TeX is in (so-called) horizontal mode, blank lines are indicators of paragraph breaks. If you don't want to generate a paragraph break, don't provided blank lines.
Add % (comment characters) immediately after the first and second \end{wrapfigure} statements. For the example at hand, this measure isn't strictly necessary, but it may come in handy for other wrapfigure widths.
\documentclass{article}
\usepackage[demo]{graphicx} % remove 'demo' option in real document
\usepackage{wrapfig}
\graphicspath{ {images/} }
\begin{document}
\noindent
\begin{wrapfigure}{r}{0.5\textwidth} %this figure will be at the right
\includegraphics[width=0.5\textwidth]{image1}
\end{wrapfigure}%
\begin{wrapfigure}{l}{0.5\textwidth}
\centering
\includegraphics[width=0.25\textwidth]{image1}
\end{wrapfigure}%
\begin{wrapfigure}{l}{0.5\textwidth}
\centering
\includegraphics[width=0.25\textwidth]{image1}
\end{wrapfigure}
\end{document}
Addendum: The wrapfigure environment isn't really meant for the type of work done in this example document. To get finer control over the positioning of the elements, I recommend you not use wrapfigure environments at all and, instead, simply place the images on the left into a minipage environment and place the image on the right in a separate minipage. The two minipage environments will automatically be centered vertically relative to each other; I think that's what you want.

\documentclass{article}
\usepackage{graphicx}
\begin{document}
\noindent
\begin{minipage}{0.5\textwidth}
\centering
\includegraphics[width=0.5\linewidth]{image1}
\medskip % note the blank line immediately above this line
\includegraphics[width=0.5\linewidth]{image1}
\end{minipage}%
\begin{minipage}{0.5\textwidth}
\includegraphics[width=\linewidth]{image1}
\end{minipage}
\end{document}
I incorperated your comments. It seems to have solved about 80% of my problem. But the first top lmage is starts a bit below than the right hand side image. It can be viewed from this image. https://drive.google.com/file/d/0B-Z4fjNozQQWM2VRc0NvSkozeGs/view?usp=sharing
– Denis Sep 04 '16 at 06:41wrapfigureenvironments to place the three images? IMNSHO, It would be much more straightforward to use aminipageto encase the two images on the left and anotherminipagefor the image on the right. I've posted an addendum to show how this might be done. – Mico Sep 04 '16 at 06:50I appreciate your time a lot
– Denis Sep 04 '16 at 06:56wrapfigureenvironments are placed on a page. I'm pretty sure, though, that it's not optimal to use them for the example at hand. With a lot of hard work and applying various ad-hoc solutions, it's probably possible to get the images to be placed exactly the way you want even with variouswrapfigures. But why pursue this approach if theminipageapproach is entirely straightforward? – Mico Sep 04 '16 at 07:01I am a full time academic. I use latex to make scintific publications and presentations. May be out of your head, you can state some obvious libraries. Then I can learn them :-)
– Denis Sep 04 '16 at 07:04subfigureenvironment (as provided by thesubcaptionpackage) is nothing but a special type ofminipageenvironment. The main new feature of asubfigureis that it provides a method for providing captions. – Mico Sep 04 '16 at 07:05