Facebook Methods description: feed.publishStoryToUser

Publishes a News Feed story to the user corresponding to the session_key parameter.

Facebook Methods description: fbml.setRefHandle

Associates a given “handle” with FBML markup so that the handle can be used within the fb:ref FBML tag. A handle is unique within an application and allows an application to publish identical FBML to many user profiles and do subsequent updates without having to republish FBML on behalf of each user. See the FBML […]

Facebook Methods description: fbml.refreshRefUrl

Fetches and re-caches the content stored at the given URL, for use in a fb:ref FBML tag. See the FBML documentation for a description of the markup and its role in various contexts.

Facebook Methods description: fbml.refreshImgSrc

Fetches and re-caches the image stored at the given URL, for use in images published to non-canvas pages via the API (e.g. to user profiles via facebook.profile.setFBML, or to news feed via facebook.feed.publishActionOfUser). See the FBML documentation for a description of the markup and its role in various contexts.

Facebook Methods description: auth.getSession

Returns the session key bound to an auth_token (as returned by facebook.auth.createToken or in the callback_url). Should be called immediately after the user has logged in. See the authentication guide for more information.

Facebook Methods description: auth.createToken

(Intended for desktop applications only.) Creates an auth_token to be passed in as a parameter to login.php and then to facebook.auth.getSession after the user has logged in. The user must log in soon after you create this token. See the authentication guide for more information.

Facebook Methods description: marketplace.removeListings

Remove a Marketplace listing.

Facebook Methods description: marketplace.createListing

This method allows you to create and modify Marketplace listings.

Facebook developer: How to Write a Facebook Application in 10 Minutes

I found on gathadams.com this nice tutorial will help you to develop an application like a guess game in only 10 minutes
Ready to start the chrono ?
So here are the headers:
1. Create your demo page. (it should take 2 minutes)
2. Install the Developer Application. (it should take 1 minute)
3. Create the Application. (it should take […]

Facebook Methods description: notifications.search

Will search the logged in users’s networks for listings matching the category, subcategory, and query provided.