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Sinatra: Up and Running is organized as follows.
Chapter 1, Taking the Stage, serves as a high-level introduction to some of the core concepts in Sinatra. It also discusses how to install the Sinatra gem, and walks through the creation of a simple application.
Chapter 2, Fundamentals, covers the different features of Sinatra, such as route definitions, creating views, managing sessions, and so on. It also serves as something of a reference chapter, with each topic discussed in granular fashion.
If you’ve already built some Sinatra applications of your own and are fairly comfortable doing so, you can likely just skim through Chapters 1 and 2, although the newest release of Sinatra (version 1.3.1) contains a number of changes that are worth exploring (including support for the HTTP PATCH verb, streaming, etc.).