Is it possible to develop a SharePoint solutions in local machine,Without installing SharePoint Server
As per your question you have used to difference words. Let me explain both.
how to deploy a SharePoint solutions without installing SharePoint? : No you cannot deploy solutions if you don't have SharePoint in your development system.
Is it possible to develop a SharePoint solutions in local machine, : Yes it is possible to develop, you need required dll's to referenced. But it is a big pain developing code without SharePoint. As after every change you will have to copy the
wsp manually to the server where you have SharePoint, and then deploy using
no, it's actually not possible.
There are some tries on the internet with which you are copying Keysets from Registry from the Server with the installed Sharepoint to your PC. But these approaches doen't work at all. (Self tried them...)
So you have to install your Visual Studio/IDE on the same machine as SharePoint because the IDE checks even in the Solution Creation Step if there is a available SharePoint Installation on your machine.