Update: There is now a much more detailed post written during the Severless Conference in may 2017

The following links will help you get up to speed and keep informed

Serverless with Azure

• View a short slide deck introducing serverless with Azure
• Explore the Azure features for Serverless
• Thorough article on Serverless Architectures

Functions

• Watch Scott Hansleman’s short  – more videos in this post
• Watch Chris Anderson’s deep dive into Developing Azure Functions, with Jeremy Thake
• See the Overview on the main Functions page
• Explore Functions without an Azure Account and follow a detailed walk-through
• Read the in-depth Documentation
• Get help on StackOverflow or possibly MSDN forums
• Collaborate on the Functions GitHub Repo

LogicApps

• See the overview on the main LogicApps page
• Monthly
• Catch up with the team Blog
• Suggest and Vote for features on the UserVoice
• Collaborate on the Logic Apps GitHub Org

More

has a useful curated collection of links on Azure Serverless