There are many great resources for learning Xamarin, ranging from docs, samples and videos, to full-blown training via Xamarin University. If you’re just getting started, here are a list of resources to get you off to a good start. There are many other articles and samples as well in the Xamarin Developer Center, so it really depends upon your interests, but these are good fundamental topics in any case:

Xamarin.iOS:

• http://docs.xamarin.com/guides/ios/getting_started/
• http://docs.xamarin.com/guides/ios/user_interface/introduction_to_storyboards/
• http://docs.xamarin.com/guides/ios/user_interface/tables/
• http://docs.xamarin.com/guides/ios/user_interface/introduction_to_collection_views/
• http://docs.xamarin.com/guides/ios/platform_features/introduction_to_ios_7/

Xamarin.Android:

• http://docs.xamarin.com/guides/android/getting_started/
• http://docs.xamarin.com/guides/android/user_interface/working_with_listviews_and_adapters/
• http://docs.xamarin.com/guides/android/platform_features/intro_to_content_providers/
• http://docs.xamarin.com/guides/android/platform_features/introduction_to_ice_cream_sandwich/
• http://docs.xamarin.com/guides/android/platform_features/introduction_to_jelly_bean/
• http://docs.xamarin.com/guides/android/platform_features/introduction_to_kitkat/

Xamarin.Forms:

• http://developer.xamarin.com/guides/cross-platform/xamarin-forms/

Also see:

• http://docs.xamarin.com/guides/cross-platform/application_fundamentals/building_cross_platform_applications/
• http://docs.xamarin.com/guides/cross-platform/application_fundamentals/pcl/

And check out the recipes, samples and videos sections as well:

• http://docs.xamarin.com/recipes/
• http://docs.xamarin.com/samples-all/
• http://docs.xamarin.com/videos/