This article explains how to import your Outlook.com messages and contacts, including data from a Hotmail or Windows Live email account, into Gmail. You'll need access to the desktop version of Gmail to complete this transfer.
How to Import and Export Contacts in Outlook
Before you begin the import process, prepare your Outlook.com account by copying any messages you want to keep from your Deleted Items and Junk Email folders to your Inbox (there may not be any messages in these folders that you want to keep. After all, these are folders where you usually only keep emails that you want to delete and don't need, but just in case).
To migrate your Outlook.com messages, folders, and address book contacts to Gmail, follow these steps:
On your Gmail account page, select the Settings button in the top-right corner of the page (it looks like a gear icon).