I don't know how to put up this question but have tried my best to do so.

I need to transfer or convert the emails from my microsoft outlook 2011 to apple mail, both running in mac book air.

Also there are some selected contacts and a whole calender entries that are required to be migreated from outlook 2011 to apple mail.

I was suggested to post my query here, and hope to get the right solution for transferring or converting the data from outlook 2011 to apple mail.

Thank you for all your help. 

You are far more likely to get a better/faster response by posting your question in a forum dedicated to Outlook 2011 since that caters to the Apple based demographic

Office for Mac
http://answers.microsoft.com/en-us/mac/forum/macoffice2011-macoutlook?tab=QnA&status=all&mod=&modAge=&advFil=&postedAfter=&postedBefore=&tm=1374574972930

(as for "don't know how to put up this question....." - stated requirement is clear, concise and to the point so anyone familiar with both O'2011 and Apple Mail should be able to easily point you in the right direction fairly quickly)

For mac to apple mail transfer, you need to do a small job just convert files from outlook 2011 (olm) to apple mail (mbox) compatible format. 

You can check Here: Click Here

There were some similar queries here:-