Is any other open source web server available  other than Apache webserver for web application development?
Apart from Apache web server is there any open source web servers available for web application development? are you looking for an HTTP server or a web framework, the two are quite different.
HTTP servers simply send/recieve requests among other tasks, yes you can use PHP and other tools most commonly through CGI or FCGI but fundamentally an HTTP server simply accepts HTTP requests, some content maybe dynamic if its coming from an underlying framework.
A web framework is a collection of tools used to generate dynamic content, or web apps, many frameworks come with a built in http server so you don't have to configure one on your own, but they aren't as powerful or as robust since the underlying frameworks tends to concentrate on generating the content.
nginx is one my favorite HTTP servers, among the many out there, since it tends to be one of the easier ones to configure.
As for web frameworks, there are many many out there, in the python comunity (giving the python tag) django tends to be quite popular since it tends to include virtually all the tools you'd ever need to deploy a web app, which include, url dispatchig, database engine + ORM Object Relational Mapper and its own templating engine to render dynamic html in its own limited language, to remove as much as possible the logic from the rendering phase.
Usually django apps are deployed behind nginx, to control multiple instances of sites on the server, as well as serving static content, web frameworks are not great at it.
Theres also micro-webframeworks like bottle which is basically a single python file, its quite cool, I usually use sqlalchemy as the ORM when building simple bottle apps.
Apart from Apache web server is there any open source web servers available for web application development? 
I am looking for a web server developing python web applications and deploy it and test it.