I am new to Git.
Is the installation for Git server same as how we install on local machine?
I am finding a GUI Git installer for server, I found one http://gitstack.com/, but is there a any open source one?
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No I would not say that. Although there is a number of ways to share a git repo hosting a central server usually differs from it.
So beside using SSH connections to share a repository I went the Subversion approach using HTTP - it is in my Opinion the easiest way to access a repository without managing SSH keys. On Linux people may be more fit with that but not every developer has a talent for that.
So you could use Apache HTTPD and DAV to host a repository: http://techblog.zabuchy.net/2012/git-server-with-apache-authentication-on-ubuntudebian/ This is for Ubuntu but the modules are available on Windows too. Most self-hosting solutions are based on Apache HTTPD and a module. (But most of them are Linux focused, Windows is not that common for this)
There are products like Atlassian Stash http://www.atlassian.com/software/stash/overview that are even more comfortable.
But some people even integrate it into CollabNet: http://dylanbeattie.blogspot.ch/2011/02/how-to-host-git-in-same-apache-server.html
So with Apache HTTPD you should be able to build cost friendly solution.