Invitation Letter to bring my mother on visit visa.

A Portuguese does not need a visa or invitation - she can just come and stay with you!
(In case your mother is not Portuguese, which you did not mention, the situation might be different. In that case she should contact her nearest German embassy, where she intends to apply for the visa, to ask about the requirements.)

As beppi said, if your mother is holding Indian passport, she can work with the consulate office that has jurisdiction of the state she lives in.

http://www.vfs-germany.co.in  is the starting point. Select the consulate office and it will lead you to the visa process page.

Example: http://www.vfs-germany.co.in/mumbai/tourist.html

checklist: http://www.vfs-germany.co.in/mumbai/pdf … _visit.pdf

Information available in VFS website is very comprehensive and clear.

Invitation letter samples: You can get plenty by googling "sample invite letter for german family visit visa" .