If you want an excellent introduction into Windows Azure I can recommend “Windows Azure: Step by Step” from Roberto Brunetti. This book will teach you the basic components of Windows Azure and how to build an application with them. It will introduce you to Azure Compute, Azure Storage and Azure AppFabric Servicebus; in clear and easy-to-follow step-by-step instructions you build applications that use the different Azure features. In my opinion this is the best way to learn.
Unfortunately this book doesn’t have space to delve deeper into some subjects (or you would need a >1000 pages book), so if you want to learn more about all the other things I recommend our Azure training.